Rory McIlroy, not surprisingly, has a priority of targeting the Majors each season but also has a number of non-Major tournaments – among them this week’s Memorial at Muirfield Village in Dublin, Ohio – elevated to a special wishlist of his own.“I would say here and Tiger’s event at Riviera [the Genesis Invitational], they’re the two that I would love to win,” revealed McIlroy, playing for the first time since the US PGA Championship and for the only time ahead of the US Open in a fortnight’s time, adding:“I’ve been lucky enough to win [the Arnold Palmer Invitational] at Bay Hill, but not while Arnold was alive. So I always thought it would be cool to win here and take that little walk up the hill off the 18th green and shake Jack’s hand. Also, Jack and I share a nice history. I’ve known him for nearly 20 years. He’s been nothing but great to me and my family. This is certainly one I would love to get done.”McIlroy’s decision to pick-and-chose his scheduling has resulted in fewer long stretches of events. Indeed, his time since tied-seventh at the PGA at Aronimink was spent with wife Erica and daughter Poppy in settling into their new house at Wentworth, and then paying a reconnaissance trip to Shinnecock Hills on Monday to prep for the US Open ahead of arriving to Muirfield Village.Although he didn’t play last year, the Northern Irishman’s previous four appearances in the Memorial delivered four successive top-20s with a best finish of tied-seventh in 2023.“For it being such a long golf course I feel like it takes driver out of my hand a lot, which, you know, I pride myself on that being one of my biggest weapons. The fairways pinch in right around the spots where I would be finishing driver. It’s frustrated me in a way that I feel like my biggest weapon is in some way neutralised here.“And then I have to play the golf course like most of the other guys in the field, everyone plays from the same spots. It’s more that there’s bunkers that I think I can carry that I could get an advantage, but there’s really no advantage to it because, obviously, the rough here is so penal, and then the angles into greens. It’s just about me being a little more disciplined and not being so aggressive with my strategy,” explained McIlroy of bringing a different strategy and a more patient outlook in his bid to deliver a win in the event.Shane Lowry at Muirfield Village last year. Photograph: Michael Reaves/Getty Masters champion McIlroy and Shane Lowry are the two Irish players in the field, with the pair having set out different schedules in the weeks ahead: while world number two McIlroy is playing the Memorial and then reappearing at the US Open, Lowry is on a four-week stint with one eye on moving up the FedEx Cup standings to get into all three playoff tournaments.Lowry, currently 52nd on the FedEx Cup standings, has pencilled in an itinerary that has him playing at the Memorial – where he was tied-sixth in 2021 – followed by next week’s RBC Canadian Open, the US Open and then The Travelers before moving back to Europe ahead of the Scottish Open and The Open at Royal Birkdale.“I want to do well in the FedEx Cup. I probably need a couple of good weeks in that to jump up because my plan is not to play much golf in the summer, so [this] stretch of four weeks will be pretty important for that,” said Lowry following the PGA. He is re-emerging from a two-weeks break since then, with the family – wife Wendy and daughters Iris and Ivy – accompanying him for this stretch of events.LowdownsThe MemorialPurse: €17.25m/$20m (€3.45m/$4m to the winner)Where: Dublin, Ohio, USAThe course: Muirfield Village Golf Club – 7,569 yards/par 72 – is affectionately known as “Jack’s Place,” being owned and designed (in collaboration with Desmond Muirhead) by none other than the tournament host Jack Nicklaus. The venue’s name is inspired by Muirfield in Scotland, where the Golden Bear won the first of three Opens in 1966. The course, which opened in 1974, has undergone renovations in recent years but retains its reputation as being tough and demanding, known for its heavy rough and quick greens.The field: Another of the new PGA Tour designated tournaments with a $20 million purse, nine of the top-10 players on the world rankings, headed by Scottie Scheffler, are playing this week with number seven Collin Morikawa the notable absentee. Scheffler is the two-time defending champion and looking for a three-peat in the tournament, a feat last achieved by Tiger Woods (1999-2001). Tony Finau, Patrick Rodgers, Bily Horschel and Matt Kuchar have received the sponsor exemptions into field.Quote-Unquote: “The last two years don’t mean much when you stand on the first tee, but this is a golf course I’ve had some success at and this will be a cool place to be able to accomplish something like winning the same tournament three years in a row, especially with it being Jack’s Place ... the golf course is already firming up pretty good. It doesn’t look like we have much rain in the forecast, so it should be another pretty challenging week” – Scottie Scheffler on chasing a three-peat.Irish in the field: Shane Lowry kick-starts a four-week stint on the road here (with the Canadian Open, the US Open and the Travelers to follow) and is paired with South Korean Sungjae Im in the first round (2.30pm Irish time). Rory McIlroy didn’t play last year but returns looking for a first win at Jack’s Place and is paired with Justin Thomas (3.25pm Irish time).Betting: As it usually is these days when both Scottie Scheffler and Rory McIlroy are in the field, the duo head the market: the American is rated 11-4 favourite, with McIlroy a 10-1 chance. Ludvig Aberg has been in great form this season and is available at 12-1 while US PGA champion Aaron Rai is available at 50s.On TV: Live on Sky Sports+ (from 12.45pm).US Women’s Open presented by AllyLeona Maguire tees off at Riviera this week. Photograph: Harry How/Getty Purse: €10.4m/$12m (€2.07m/$2.4m to the winner)Where: Pacific Palisades, California, USAThe course: Riviera Country Club – 6,699 yards/par 71 – is a classic course originally designed by George C Thomas jnr and William P Bell, although it was modernised in the 1990s by Ben Crenshaw and design partner Bill Coote. Located in the Santa Monica Canyon, a short distance away from Sunset Boulevard, the course is hosting a women’s Major for the first time. The fourth hole – 192 yards – was considered by Hogan to be the “best Par 3 in America.”The field: A stellar list for the second Major of the year on the women’s circuit, headed by world number one Nelly Korda. Sweden’s Maja Stark is the defending champion. The 36-hole cut will feature the leading 60 players and ties. Should there be a tie after 72 holes, a two-hole aggregate playoff will take place immediately following play.Quote-Unquote: “I would say Major championships should always test every part of your game when it comes to hitting the fairway being a key, growing out the rough, distance, the firmness and the speed of the greens. But it should also play fair. From what I saw, it checks all the boxes” – Nelly Korda on the examination posed by Riviera.Irish in the field: Leona Maguire had a second top-10 finish of the season in last week’s ShopRite and will hope to carry that momentum to Riviera, where she is in a group with Steph Kyriacou and Ina Yoon (3.40pm Irish time); Olivia Mehaffey is back in the championship for the first time since 2020 after coming through qualifying and is grouped with Becky Morgan and Ina Kim Schaad (4.35pm Irish time).Betting: No surprise that Nelly Korda – who has three wins and three runners-up finishes in seven outings so far this season – is the market leader at 7-2 ahead of Jeeno Thiitikul at 9-1 ... Lottie Woad is worth an each-way look at 30-1 while Casandra Alexander at 80-1 is another each-way prospect.On TV: Live on Sky Sports Mix (from 7pm), Sky Sports Main (from 10.15pm).