The other coastal town you could visit could be Brighton, it is further away but it takes about the same time to get there because the Thameslink railway have class 700 type trains. I'm a fan of the Thameslink railway, they pushed the limited infrastructure as far as it would go and made sure all their trains could trump the speed caps on all the rails. They must have poured a lot of investment into the franchise because they have a huge operation zone, you need a lot of rollstock to pull that off, all their trains are overhead power high speed electric class 700 type trains, robust and reliable and fast. There are several stations you can get a Thameslink from, Farringdon, London Bridge, Black friars.
If you just want to enjoy London then I would recommend walking along the Thames (🗣️Tems) river. Most the important places are around there. There are also two large amusement parks in London 'Chessington world of Adventures' in the south and 'Thorpe park' on the western edge, they're not straightforward to get to without a car unfortunately. I think there is a shuttle bus from 'Stains' train station to Thorpe Park. You could get an Uber from Chessington South train station or walk it from there.