God yes. When I was in law school I'd either be out with straight friends at straight bars, or I'd be going off alone to the gay bars/clubs.
Straight people don't really go out alone. That's considered weird, odd and creepy. Unless maybe it's a dive-bar during happy hour.
Gay people go out alone all the time. I've gone out for almost 9 years in a row in cities across the country (LA, NYC, SOBE, Philly, Raleigh, etc) and about 20% of guys show up alone at drag show / piano bar type places, and in large dance clubs as many as 33% of the guys enter alone. Fewer leave alone, obviously.
In LGBT bars/clubs it's really not considered weird at all. In fact, if you're young and/or cute (don't call me shallow, I'm simply telling the facts of life for how society will perceive a person) then you'll make friends REALLY quickly. My first night in a new city/bar used to go something like this:
(1). Get ready while I pregame with a few beers or mixed drinks.
(2). Walk or get a taxi to the bar/club. Do not drunk drive.
(3). I'd get really nervous from the time I left my place until about 15 minutes after entering the bar. Just try to be confident, pleasant and smile. Order a drink. Take a smoke break if you smoke. Just try to not stand alone in a dark corner. Make small talk with other guys who are there alone--even if you don't want to sleep with them. First, it relaxes other people because it shows you're not shallow and will talk to anyone. Second, it will give you people to bounce around from. Before you know it, you'll have four or five people/groups that you're bouncing between. If/when you repeat, you'll find that certain people/groups are always there, and your hard work is already done. There's really nothing to it.
Go and have fun. Just don't drunk drive.