Some random stuff off the top of my head
I really like
Oakland and the East Bay in general. Just north of Oakland you have Berkeley. It has a great college town vibe but is also very easy to get to San Francisco. Doesn't seem like the Cal Bears are playing when you might be in the area unfortunately, but it is worth a visit or maybe to even stay there.
San Francisco is a great city. Seems pretty hard not to like it. It is very expensive these days, hence a lot of people live in the East Bay over in Oakland. It is very easy to get over to SF from Oakland on the BART train which runs until about 12:30am. Oakland has a lot going for it, it has a rep for being rough and yes, certain areas are, but I guess that's the same in all US cities. I think the Raiders are a pretty unique team and the fans really go for it. The stadium is old and crumbling and not one of these new arenas. There's a lot going on in Oakland as many of the Bay Area creative people, musicians etc live over there now as they can't afford SF rents.
I'd also recommend a baseball game in San Francisco. The Giants have the best stadium that I've been to so far in the MLB, just at the harbourside.
I loved the Amtrak train ride from LA up to SF and would recommend it. Parts of the journey go right along the coastline, so take a seat on that side of the train if you can. If you wanted to break the journey up and stay somewhere along the way I would highly recommend San Luis Obispo. It is a smallish town/city with a university there. It is a kind of sleepy/surfer style town and I think a great place to stay a day or two. Santa Barbara would also be another good place to spend a night.
In
LA you will find it most tricky without a car. There is public transport but it isn't very integrated and is also sometimes hard to find out the info about it. Also LA is massive so lots of taxis aren't necessarily financially practical. Almost all transport terminates or goes through the centre of downtown, there is a light rail that does through Union Station. Downtown itself isn't great but I guess I might try to stay somewhere near there. For example Little Tokyo (Japantown) is very central, as is what they call the 'Arts District' Your other option would be go for the LA beach experience and pick somewhere near the ocean. Santa Monica or Venice for example. Great places, but limits your possibilities of getting around the city without a car as you are in the edge of the city and it could take your several hours to get across town.
San Diego is a nice town. Daytrip to Tijuana Mexico recommended, just down take many/any valuables! You can take the trolleybus down to the border and then just walk over. It is quick going over to mexico, there may be a queue on the way back but it is much quicker than in a car.
Most/all cities have First Friday each month where all the art galleries open up and everyone drinks loads of booze and goes round the galleries. LA and Oakland ones recomended. Liking art is optional, they are social occasions!
Live poker. You didn't mention this but there are a bunch of places to play live poker in
, unfortunately most are in ghetto areas. I'd recommend a trip to Commerce just to see the biggest poker room in the US (the world?) - the action is amazing here. Rake is pretty low, but unlike Vegas where they take it out incrementally, in LA they just take it all ($5) on the flop, so this can be a bit annoying and can make $1/$2 more expensive for example. If you have a big MTT cash you will be liable to California state witholding tax which I think is 5%. I'm not sure what the lower limit is. It might be 1k? but it is worth investigating if you play any live mtts as this is hard/impossible to get back.
The Bike is the second LA casino - it has a reasonably cheap hotel over the street.
New Orleans has a casino directly downtown, so this might be one of the easiest places to go and gamble without a car on your trip.
AccomodationI can't say enough good things about Couchsurfing. You make a profile with info about yourself and you find cool/interesting people and ask to stay on their couch or sometimes a spare room. I met a bunch of interesting people in this US couchsurfing. I ended up going to some places I'd never have gone to (High School Prom, Haunted Mansion, Cupcake baking contest, housesitting rabbits and getting to stay at an apartment for free). I mixed couchsurfing with hostels. There are good hostels and bad hostels and I guess it is also the luck of the draw on who your room mates will be.
Airbnb is another great option. You can often rent people's spare rooms for affordable prices. If you stay somewhere for a week you can sometimes get a 10-20% discount too, so makes the 7th night free.