When my husband and I met, he was 21 and I was a few months shy of my 21st birthday. It never really was a problem. If there was a particular bar he wanted to go to, he would save it for a night when I was busy (studying, rush, made plans with my sisters/friends, etc) and he'd go with his friends. Also, some bars/clubs have 18+ or 19+ nights, so we'd go on one of those nights. Some of the trendier clubs in Boston are actually 23+, so he felt my pain because he couldn't get into them either!
See if you can convince him to take you to bars that have attached restaurants. If you sit in the restaurant section, they don't care how old you are (this may vary by state). It's not quite the same as being physically "at the bar", but he can have whatever he wants to drink, you can be his designated driver if need be, and it's a lot less smoky
