This is too late, but I figure it wouldn't hurt to post since other people might be interested in the future.
There is a gastropub in Belmont Shore area of Long Beach called Tavern On 2 that has a good selection of belgian ales. Their food is okay. They opened a little less than a year ago and I have only visited once.
Congregation Ale House (downtown) also has a stellar selection of beer and also serves food. I visited for the first time earlier this week and I do expect to go back soon. I'd recommend.
Breweries, there is Rock Bottom Brewery in Downtown that has a good selection of microbrews. I have been here quite a few times. Their brews are a hit and miss, but overall I would say it's worth checking out.
Belmont Brewing is also in Belmont Shore and they have a fantastic stout called "Crude." A couple of my stout enthusiast friends really do love it.
As for markets, I highly recommend California Heights Market in Northern Long Beach. It's kind of a small market so it doesn't seem like much, but once you step inside you'll see it jammed packed full of various beers. Best selection in town in my opinion. It's the only place I have found in South Bay that hasn't given me the run around with Pliny The Elder (kind of a hard find). The first time I went there and asked if they had it, the clerk smiled and got it for me from the back. The only problem is it's a bit of a distance from the Westin, so if you have a rental or ride I'd say go for it.
As for markets in Downtown, I can't really help you there because I spend most of my time on the other side of town.