Is there a nice bar in Long Beach?
320 Main in Seal Beach. Finally a serious mixologist in the area. Fine cocktails, well prepared (and regular old drinks too), and still casual and friendly. Full restaurant as well. (I've only had apps, which were quite tasty).
Around 2nd St there's a hideous dearth of decent, adult bars. Besides those already mentioned, both Bono's and Nico's have small full bars; Kelly's in Naples serves mammoth Martinis to a mature crowd. Up by the pier there's Belmont Brewing Company (which might not qualify as divey, but doesn't qualify for much better. Gets a college-y crowd); and La Palapa which books the worst music ever but has a decent beachfront atmosphere. I'm still looking for the one that fits me perfectly, so far 320 comes closest. But one of these might work for you. Let us know.
25 39th Place, Long Beach, CA 90803
4901 E 2nd St, Long Beach, CA 90803
La Palapa Restaurant
2222 E 7th St, Long Beach, CA 90804
You are right about the bars--you will probably have to go to a restaurant with a good bar area. The Madison in downtown LB has a great bar area that feels pretty separate from the main restaurant, meaning you don't feel like you are supposed to be waiting for a table. The Observation Bar at the Queen Mary is pretty cool, too (although I haven't been there for a few years, admittedly). Michael's in Naples has great appetizers but I wouldn't call the bar "relaxing" as I didn't think the furniture was very comfortable :) Tantalum has a pretty good bar as well.