I grew up in Bath and only moved out of the city 2 years ago (I'm 37) so know it quite well!
There is the Thermae Bath Spa which has a rooftop pool - it is quite expensive (something like £19pp for an hour) but they do offers in the evening I think for groups with prosecco etc.
In early September you may still have some warm weather so if you wanted something cheap to do you could go for a picnic in the park by the Royal Crescent where you could take in some of the architecture - it's only a 15 minute walk from town up a not too steep hill and would mean you could see both The Circus and The Royal Crescent on the way. There is also a nice pub called The Marlborough Tavern where you could eat/have a drink.
Food wise there is loads but I'd recommend Beckford Bottle Shop or Corkage which both do small plates and wine by the glass so people can order as much or as little as they want. For a treat/more expensive meal Hudson Steakhouse is amazing!
To be honest Bath City centre is pretty small and flat so assuming everyone is in at least average health you could walk around and catch most of the sights (Bath Abbey, The Circus, The Royal Crescent) without having to pay. There is a sightseeing bus if people can't/don't want to walk.
For more "touristy" things you could go to the Roman Baths. The Pump Rooms I think is overpriced for what it is (essentially a cafe attached the The Roman Baths) and there are a lot of cheaper/nicer ones including Sally Lunns which is down a lovely cobbled street by the Abbey courtyard and you can buy the compulsory "bath bundle."
If it were me though and the weather was nice I'd just go for a slow meander through the city calling in at cafes/bars (depending on which way you're inclined!) or one of the many parks in town (Parade Gardens is lovely by the river and adjacent to Pulteney Bridge and the weir which are both very picturesque!)