I've played on some flag football teams associated with Houston Sports & Social Club. I had fun and there wasn't any stupid drama like you see in more competitive leagues (i.e. no fist fights or excessive cursing towards refs/players). The club also has softball teams and you can sign-up through their website. All of the teams are co-ed and made up of mostly 20-30 year olds.
We play through Houston parks and rec. They have several fields across Houston, so there's bound to be one convenient (make sure you pick one that allows alcohol).
It's a 5 week format, 2 games a night earliest and 6:30 and the latest at 9:30. Been playing through them for about a year and half now, no major complaints.