a weekend out of London

Bath would be good , The Cotswolds are best with a car . Consider Cambridge , a university town with a panoply of English architecture and the bucolic rural serenity of the Cambridge Backs

What time of year?

You could go to Oxford and take a one-day van tour of the Cotswolds. The companies GoCotswolds and Secret Cottage run tours out of Moreton-in-Marsh, which is a short train journey from Oxford. The tours depart from the Moreton train station. Moreton is sort of the bus hub for the Cotswolds, so if you're hikers you might be able to stay in Moreton and do a day's walking, returning by taxi if necessary.

Although I enjoyed the two museums I visited in Bath, I wasn't interested in the Roman Baths and am not a Jane Austen groupie. I found the architecture boring after the first few blocks of seemingly identical Georgian row houses. I was happy to leave after a day-trip--very different from my reaction to Oxford. It's all a matter of taste. But there's a company (MadMax) running tours of the Cotswolds from Bath, so you wouldn't necessarily need to fill 2 full days with Bath sightseeing.

I prefer Brighton to Bath but imagine I'm in a small minority there. Brighton's good for more than half a day, I'd say, then it has at least two nice day-trips, to Lewes and Arundel.
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Bath and the Cotswolds would bore an average 11 year old rigid.

Brighton is easily reachable by car and has plenty to occupy you all. Brighton Pavilion for history, the Lanes for antique shops, unique gifts and some great independent cafes (Kemp Town area is also good for foodies), a great aquarium, walk the pier, the Toy and Model Museum and visit nearby Lewes if you want to see a castle.

York would be a better option than the Cotswolds or Bath for an 11 year old IMO.

Agree with what others have suggested. When I was 11 years old I would not have appreciated being taken to Bath or the Cotswolds. Why not look at York. Easy train from Kings Cross and lots to do - Minster, Railway Museum (surprisingly brilliant museum) , walking the walls etc.

What's the rationale behind those three choices? There are many, many more destinations that may be more appropriate depending on interests, time of year etc.

For me Bath would be the most interesting but I'm 43, I love Roman history. Tea rooms, antique shops and hikes through muddy fields are not my thing and whilst I enjoyed Brighton in my late teenage years it no longer has the same attraction. As you can see, it's all entirely subjective.

I've driven through the Cotswolds on a number of occasions en route to various places and never felt compelled to stop and gaze in awe at the area, it's not much different to many other places in the UK so whilst I can appreciate its atractiveness I cannot understand the obsession it's generated for many Americans. An 11 year old is likely to be bored as hell there.

these are great responses
this will be for the last weekend in July
the rationale with those spots is because the following week I will be taking her to Edinburgh and hopefully stopping in York on the way. So we have a weekend to travel with dad and wanted something easy to do from London where my husband is staying.
Seems Brighton is a good choice and I haven't been since college so that might be fun. But really I am open to anything just not too far north since I will be doing that days later

There seems to be a consensus that some of these places might be boring for an eleven year old . While that may be true , it might be a wise choice to take some chances , and test a child's level of curiosity , it might have a positive impact as they mature . We used to do this when our children were little , always took them to museums and historic sites . Obviously we never made it an onerous , one sided affair , and laced things with visits to the beach and venues appropriate to children . But , now , as adults , it paid off , and they lead richer , more varied lives as a result . As the writer Dorothy Parker once said - " The cure for boredom is curiosity , there is no cure for curiosity "

Never heard that Dorothy Parker quote, but I love it!

I'd say Bath if your daughter is at all interested in history or architecture. The Roman baths, one of England's best late-gothic churches, all those Georgian facades (sorry, acraven). And Mad Max Tours is supposed to be very good, with various choices depending on your (and her) interests.

Brighton is a fine seaside resort that will presumably be very crowded on a July weekend.

I hesitate to suggest a quick trip by Eurostar to Paris, because Paris obviously deserves a lot more time. But a weekend would be better than the one-day round trips some people try. It's expensive and a lot of work but it's Paris after all.

Ah, now we have narrowed things down a bit. A young girl's interests are likely to be different than a boy's interests of the same age so what are her interests?

she's up for anything though we like to explore outside and walk around. less museums. Brighton seems like a great and there is always the beach to spend time on. there will be crowds everywhere.BUT if there is another place in England that would be fun
please let me know
we have already been to Paris with her and though I LOVE Paris I'd rather find something to explore in England

I would add in Liverpool as it might please everyone in the family.