Wow, OP. I could have written this post a several years ago. We even share the same hometown. I moved back to NYC after my LA stint, but I do have some advice for you if you make the move.
1. The poster above about LA's job market is spot on. Make sure you have all your moving expenses covered and a good amount of savings if the job doesn't work out. PLus so many people are out of work there, it's worse than other areas of the country. In New York, it's much easier to get work, and make more money. LA just seems difficult workwise - so make sure everything is solid with the small firm you will be joining.
2. You will save a ton of money on rent! For what you're paying for your east village studio, you can get a great one bedroom and still be saving a lot of money every month.
3. You really need to rethink the car situation. Seriously, you will need a car, but you can survive without one. It will not be easy. If you're working downtown, I don't suggest living downtown, it's a horrible area to live. If you want shops, and places to walk to I suggest living between Santa Monica Blvd and Frankin around La Brea and Highland. It's a cute little nook of an area (La Brea isn't that great though) where you can at least walk around and get to a grocery store, bars and nightlife are right there too.
You also will be walking distance to the Hollywood/Highland subway which will take you right to work downtown.
You will also be walking distance to the bus line (Santa Monica Blvd) which takes you right into WeHo, Silverlake - and all the way down to Santa Monica for when you want to hit the beach.
That's probably the best area to be if you need public transport to get to work.
I do seriously suggest getting a car though (and license) if you plan to stay.
LA is not like New York, but the weather is warm, it's very pretty - it's very different. As far as meeting people, just like anywhere else - you have to seek that out. It can be a very superficial self absorbed place to be, and you will find many of these types there so keep that in mind - but you can make quality friendships there like anywhere else. Just get involved, be social, and seek out the right people.
Good luck OP!