Could be wrong, but I don't think any of those towns are great for punting - have only punted in Reading & High Wycombe, and that was years back.
Southampton is probably the best of the bunch, there often seem to be good reviews on the SE board.
Reading seems to have a reputation as a punting desert, even though it's a city sized town with affluent suburbs. The reason might be it's White Knight central. They literally have a place there called 'White Knights Campus' - I drove past once and was horrified to see there's large grounds with many buildings - there probably thousands of them.
It wouldn't surprise me if the WKs "protect" Reading WGs from genuine punters by getting them off Adultwork & having them only advertise on their private White Knight only forums.
Three bits of advise for you:
1) In any of those towns it still might be worth having a quick search on the day, you might get lucky, I'd guess they all have a few good WGs or new ones arriving on tour etc.
2) If you have an AW account with some feedback & you know what town you're staying at in advance, maybe put out some reverse bookings. This might be especially good value say if you wanted a 1 hour dinner data / 1 hour sex type arrangement, sometimes WGs from the surrounding area seem to put in cheap bids for that sort of thing.
3) It sounds like you may be travelling past Milton Keynes, that would be a great place to stop for punting if the logistics work. You have the very reliable Milton Keynes Escorts & Annabelles if you can make between 11:00 - 20:00, & there's lots of Adultwork lasses in that town.
Happy punting