Are there any tours that are highly recommended to book ahead for Budapest in mid September?
Joan, we were recently in Budapest and had booked the Parliament Tour online. I bought our's about 6 weeks in advance. The timed tickets sell out quickly especially if you want the English version. It was a great tour. www.jegymester.hu
To Janis' point, I was there last mid October and many English tours had sold out in mid September.
If the English tours are sold out, you can try budapestrivercruise.com, they sell a combo ticket of a Danube cruise + the parliament tour (same one as booking direct on the parliament web site). You can take the cruise at any point on the same day as your parliament tour, so it’s reasonably flexible.