I you have a 17 year old daughter who loves places like Haight Ashbury, Berkely, Ca., shopping, people watching, reading, music.
What day trip from London would you take?

For those sorts of urban things, your best bet is just to stay in London. There are lots of great places all over the UK but the best shopping/people watching/music/Haight Ashbury-ish places are right in London.

If by Berkeley you mean a great university - then Oxford or Cambridge would be good day trips. But if by Berkeley you mean the young/funky vibe of the streets around the UC campus then it would still be London.

I lived near Haight-Ashbury and had gone to Berkeley undergrad, so I think the best bet would be Camden Town! Janisj is right about just sticking to Central London. If you want the H-A/Cal feel, Camden has it. It's off the Northern Line (Zone 2) ~15-20 min north of say, Leicester Square. Camden High St is crammed with shops selling alternative, psychedelic, clubby funk. The area is built around these canals (nice to walk along) and beside them are cheap food stalls from Indian curry to crepes to Asian noodles. High St becomes Chalk Farm St as you walk north and there are market stalls (Camden Lock and Stables) off the street-- jewelry, records, crafts, furniture, etc. Do be careful, as this area gets crowded and is notorious for pickpockets. If you want a break from Camden, Primrose is just 10 min away. Walk up Chalk Farm Rd to Adelaide Rd and turn left on Regents Park Rd. The short stretch has the most charming, quaint, neighborhoody feel like a Russian Tea Room, French Cafe, organic foods store, independent stores. Famous Triyoga Studio in a block away. If it's a sunny day, definitely head up the adjacent Primrose Hill for nice panoramic view of London.

Another option is the north end of Portobello Road in Notting Hill. Granted, parts of NH are upscale but it's a lovely area to walk around. From Notting Hill Gate Tube (Central Line), walk right up Pembridge Rd and veer left to Portobello Rd (the first quarter mile are the antique shops with its crowded market on Saturdays and oft-photographed pastel Victorians). Then you reach an area lined with cafes, boutiques, delis, etc. Almost daily, there is a food market. Further on, there is second hand clothing market.

If you simply want to get out of London, Brighton is probably the best easy day trip which also has the general funkiness of London's bohemian bits.

Oxford and Cambridge are sometimes even more dominated by youngish people - anyone over 25 on the (extraordinarily crowded) streets of Oxford after 1900 on a Saturday is practically run out of town on a rail. But they only really come out (from their colleges) or in (from the outlying suburbs) at night, and many Americans might be a tad taken aback by their single-minded dedication to getting totally wasted.

Hi rahjmh
I agree staying in London is probably your best bet - as others have suggested, the markets like Camden and Portobello Rd have a similar vibe to Haight Ashbury. But if you do really want to leave London, I think Brighton is the best option. It has a really nice feel to it and is on the coast. After that I'd do Oxford, with my fourth option being Cambridge. Whilst both have a young studenty feel, it's not really the same as Berkeley but still fantastic and interesting day trips. You can catch the Oxford Tube (called a tube but it's a bus) from loads of different places in central London and it's very cheap. Or catch a train to Cambridge (think you can also catch a bus, but I've only ever been by train).
Brighton is also very easy to get to by train.

It seems that half the people who've answered your question where would you go on a day trip are saying, don't go anywhere. That seems a little presumptuous, and odd.

What kind of day trip are you looking for? A train ride? Renting a car and doing it yourself? There are a lot of dogmatic likes and dislikes on this forum . . . I like Canterbury. But any town in the UK with a square and a few al fresco restaurants can be fun for people watching.

There's so MUCH to see. I went to Uni in Canterbury and it is a beautiful place to visit. Cambridge... lived there for a year, and again a great day trip. Especially on a nice sunny day. Take a picnic by the river... or on a punt!

Please take at least one trip out of London. There are so many people who don't leave London and miss out on so much.

Brighton is good too..

For a bit of culture, a vibrant town, you may be surprised by Birmingham, which is only about 1.5hours on the train.