Bath or Stratford-upon-Avon

We did both, spending two nights in each place. It's a tough choice! A lot depends on your interests. I believe that Warwick Castle is accessible by bus and if so, I'd choose Stratford because of the variety of activities available.

If you enjoy classic theatre, then the winner is Stratford, hands down! The Royal Shakespeare Company does outstanding productions there. We never miss going up for a day from London and seeing two shows. You can take a train from London and return late at night after the last show. If you go early in the morning you can also take an open top bus tour of the town and the area.

But if not for theatre, you can easily ignore Stratford's rather tacky and touristy sites and by all means go to Bath instead -- prettier town, nicer architecture, etc.

The comments above refer only to making a day trip from London. I'm not so sure that either is particularly worth it as an overnight to try to get to and from, plus make other public transport trips from as a base. I'd think a place like Dover or Canterbury might fit the bill better -- or even Brighton -- perhaps one of the Cotswald Villages (although public transport around the area is pretty difficult there, I think).

Stratford is rather poorly served by train, better, perhaps, by bus. Go for the theater, the Shakespeare sites if you're a real buff (they're profit centers for Stratford).
Bath is perhaps a more interesting city and better served by train.
Both these are doable as daytrips from London. If you want to go out of town for a few days exploration, I'd suggest traveling further afield -- to York, or Cornwall, or Wales. Decide on a town; find yourself a nice b&b, and let the proprietor help you to find your way around.

Unfortunately your choices are more limited because traveling by public transport complicates things. if you are sure driving is out of the question, then probably choose Bath. Both places have much to recommend them but getting to Bath from London by train is easier. And Bath is a great place for a day or overnight.

But another option would be to take the train to Warwick and overnight there. The Castle is wonderful and the town has a lot to offer.

A 3rd option might be an overnight in Oxford.

I'll re-enter this discussion to ask why several have indicated that it is "hard" to get to Stratford by train? I go every year and there are several trains per day direct from Paddington to Stradford. The cheap day ticket there is also a whole lot less than those to Bath.

On the other hand, I'll readily admit there isn't a lot of train service from Stratford to other locations, but the service between it and London is quite good.

I have been to both. I recommend Bath because it is the real thing. Stratford is Brit Disney.

Patrick: that is good news. the last time I tried that route I had to train to Warwick and then bus over to Stratford. But it was a few years ago and I can't remember for sure if it was because of temporary rail works.

At that time my only other option would have been to take the train to B'ham and then down to Stratford.

Definetely go to Bath. Nicer town, with great architecture. I enjoyed it because it's quite different from all cities I visited in England.

Patrick:

It is not difficult to spend the day at Stratford, or to attend a performance there. The train schedule from London coordinates nicely with performance schedules.
It would be difficult to use Stratford as a base for exploring Britain by public transportation. The train schedule doesn't coordinate nicely with much other than performance schedules.

I totally agree. I thought that's what I was saying!! Except that if you go in the morning and return in the evening, no one says you have to see a play!