Well I live in West Hollywood for about half the year, so I have to disagree with most...LA is one of the most fantastic cities in the world...but it does depend on what you like. I like music...therefore, I love being in LA.
However, you cant be staying near the hollywood sign and Universal Studios...Universal is in North Hollywood, and the Hollywood sign is on the other side of the hills, a good 25 minute drive away. Also, if you are near either of these places...There isnt a beach 12 miles away. To get to basically all the beaches, youre looking at an hour drive away to get to the beach, and about a 2 hour drive back, with traffic. If you make it to the beach, I would suggest Huntington if you want to surf, Malibu if you want to stare, and Santa Monica if you happen to be going with a girl.
Are you hiring a car? If not, you will struggle....LA is just...Huge! If youre happy staying near where youre staying, let me know where it is, and what you like doing, and I can tell you the places I would go around there. The best thing really is just to get out and about, and experience the place. If you do have a car then...West Hollywood is the place to be to party and shop. If you like rock music, get to the sunset strip, and just take your pick from the rainbow rooms, the roxy, viper room, whiskey a go go or the house of blues. All awesome venues, and live music every night at them all. If youre a big electro fan, like everyone seems to be in LA, Avalon is the place to be, which is in West Hollywood. If you like a lot of indie bands and more dive bars as oppose to wine bars, head to silverlake (If you do, I would suggest locating the Thirsty Crow, best whiskey bar in LA, and where youll find me most of the time). If you like a artsy vibe, comedy and theatre, head to north hollywood. Again, if you let me know what sort of places you like to go see I can try and recommend you.
If you want to do the sites, then you need to obviously hit up the holywood sign...my favourite place to view it is from runyon canyon (youll see a minimum of about 10 celebs walking their dogs up here..Last time I want, I accidently knocked Giovanni Rabisi over...). Youll want to head to Hollywood Blvd, to look at all the stars on the floor, along the way you can see the chinese theatre too. If you are a big film fan, head to the arclight just down the road too, awesome cinema. Food wise, make sure you hit up Big Boys, and Roscoes Chicken and Waffles...two LA staples. If you want wings...Find Big Wangs on Hollywood on a Saturday..25c wings.
Like others have suggested, if you want to get out of LA...then you have San Diego, Pacific Beach is a really nice place, but...I also find it SD a bit dull..expect a 3 hour drive. San Fran which is awesome, is at about 5 hours drive on a good day. If you are going for no longer than 2 weeks, I wouldnt go to Vegas...you need to spend a good few days in Vegas to appreciate it.
My best advice however...Find the cutest hottest girl you can...ask her for the time, and with your British accent alone...Youre a winner.
If you arent driving, be aware...that to get from say, west hollywood, to north hollywood, will set you back $50 on a weekday, more on a weekend.
Remember to tip your waitresses and bar staff well. The better you tip at a bar...the more jack youll get next time in your JD and coke...until youre drinking pure Jack for the price of a shot.