1st travel to London! (4days)

Local would depend on whereabouts you're staying.

Peruse Time Out for lots of info http://www.timeout.com/london

Yes to Bath or Cambridge (look for Advance tickets below) though you will find plenty to do in London for four days.

http://www.nationalrail.co.uk/

If you haven't been to London before, I suggest that you just focus on London rather than trying to do a day trip to Bath and another to Cambridge, as that will only leave 2 days for London. If you are flying into London from the States, your first day may be lost to jet lag. You won't find any beaches near London and a seaside trip would be a full day (that you don't have time for).

There are many good places to eat. Where will you be staying and what is your budget? (in GBP not US $). Plenty Michelin started restaurants, which will cost c £75+ per head in the evening including wine. Hummingbird Bakery is one of London's best known.

Afternoon tea at Liberty just off Regent Street is good. Lunch at RIBA on Portland Place is an interesting building (you need to book in advance).

You need to get booking your accommodation as August is very busy.

Stay in London for sure. Food/cultural experience, definately try Brick Lane at the weekend, or for just foods from around the world, Borough Market Weds-Fri, not Sat. Plan to walk everywhere since you're young and you'll find everything you're after around every corner... Except beaches, none in London. A walk along the south bank from Westminster to Tower Bridge is a must. Use trip advisor to check reviews of a restaurant you like the look of, there are thousands, wander round and see where the day takes you. I've been doing that once or twice a week for nearly 10yrs now, still not bored, still find new things. Enjoy your trip.

I think a day trip could be a good idea. Although there's plenty in London to keep you busy for four days (or four weeks or four months or four years), focusing on London will give you a one-sided view of what England is all about.

Also, London is big and busy and crowded and crazy. The only places remotely like it in the US would be New York and maybe LA. When I took my first trip to London (around your age), I had lived in Chicago for five years, and I was still a bit overwhelmed by just how much of London there was. A day trip to a smaller city or town could be a refreshing break.

As for where to go, Cambridge and Bath are both nice places, but they don't have any beaches either. If beaches are what you're after, Brighton would be an obvious choice, although it's pretty crazy too.

Like others- I also feel like you should stay in London for the 4 days. The city is huge and there is too much to do there. You don't want to leave wishing you had seen more of London.
However- if you are there on a day that a London Walk is provided, it looks like they have some good ones in August....Brighton, Cambridge and Bath included. Taking an out of London Walk to one of those places would relieve the pressure to have it all figured out yourself for a day trip out of London.

http://www.walks.com/Standalone/London_Walks_Calendar/default.aspx

Oh, and meant to mention- regarding food in London, the obvious- Borough Market.
http://boroughmarket.org.uk/

Thanks for all your great advices and informations guys :)) We're working on our itinerary in detail and am sure your precious advices helps a lot!!
And Jennifer, for restaurants/food, We're open to any price range and any style!!

Short visit, big city, stay in London!!! So much to see, do, explore. Sorry no seaside beaches but you might enjoy mudlarking ( Google).

Drinks are easy to find as pubs are plentiful and unlike American bars pubs are meeting places for families, friends, etc so don't be alarmed to see children, dogs, and grand mums and dads all gathered in a pub. Children will be gone by 7pm.

Good food is everywhere now in London. For example near St Paul's Cathedral ( one of the few buildings not destroyed in the Blitz) is a shopping Mecca called One New Change. Stellar free view of St Paul's and London for its rooftop and a potpourri of restaurants to dine at. Food trucks are also popular so check to see what ones are where by Googling Food Trucks London. Loads of websites to research. As London is a melting pot of cultures there are countless wonderful ethnic food options to enjoy. Interestingly enough last November I couldn't help but notice how many gourmet hamburger places there were so if you are jonzing for a cheeseburger don't fret you'll be able to have ones other than those from a Mickey D's or Burger King. Pub grub is tasty as well.

As far as historical sights I'm a bit bemused you asked, then again you are in your 20's. So if you know nothing about this incredible city's long history I suggest you first stop be the Museum of London. I also suggest a visit to Westminster Abbey, the Churchill War Rooms, The Tower of London, The Treasure Room at the British Library, and Greenwich.

A cultural experience can be had by participating in an evensong. Try going to St. Brides. Easier to get into than Westminsters or St Pauls . Other options are: Visiting Portobello Road Market. Although i suspect you'd like Brick Lane a bit more. 20 year olds were en mass there last visit. Going to theatre
( buy same day 1/2 price tickets at the booth in Leicester Square). Or merely wandering through one of London's lovely parks. Regents, Hyde Park, St. James, Kensington Gardens, Hampstead Heath and people watching. You can rent bikes to do this.

Lastly check and see whats happening at Wilton's Music Hall. And review Timeout Magazine online. Will tell you virtually all that will be happening in clubs, museums, galleries, etc.