We will likely fly to Manchester and play one Open course with Birkdale the leader at the moment. Then play a few other courses nearby like Formby, Hillside, and Southport with it depending on advice from the well traveled.
Mayday,
If you’re only playing one Open rota course, then go for Birkdale. It’s the best course of the three in the area.
I’d third Tony and John’s Formby recommendation - it shouldn’t be missed. It’s above Hillside, S&A and Wallasey by a clear margin. Even better if you can stay on site and play the Ladies course too. I played the main course twice and have no regrets about doing so, just kicking myself I didn’t have enough time to squeeze in a round on the Ladies course, which I hear is very good.
The other option in the vicinity just south of Formby is West Lancs, which I’ve also heard good things about but haven’t played. Will need to make a detour next time I’m passing to see it and Formby Ladies.
The Lytham stay and play package is also great and worth looking into. Stay overnight in the Dormy house and get breakfast and dinner in the clubhouse. Can either play on the day of arrival or after breakfast the following day - it‘s a wonderful experience.