2003 Battery Concerns

So it seems I ran my car out of gas (which is another problem-I have to figure out how that happened), and by doing so I drained the battery. Once we tried putting gas in it, the car started up and began recharging the battery and it is running. I then took it to get the codes checked in case a battery code came up, but the only code I got was the failure to start. (The main battery light didn't come on until after we put gas in it, and started it up one more time. Once it started to recharge, that light never came back.)
So my issue now:
The mpgs have taken a nose dive. It showed me at 39 mpg, but when I filled up I was at 34. (My gauge is usually +/- 2. 5 is a lot.) I typically average around 43-46 mpg during the summer. The battery typically displays full or one less bar. I have noticed the past few days that when I start it in the morning, the battery is not fully charged. After a few minutes though, it's back to fully charged.

I'm asking all of you wonderful people, what are my options? I've been considering taking it to Cincinnati Hybrid to get the battery tested. I live in Indianapolis.

The car doesn't feel like it's running with less power; it's just the mpg is not where it should be.

 

I've always planned on replacing the battery when it was time, and I've been warned it's coming to that age so I've been preparing. I just wasn't sure if it is time for it to be replaced or if there's anything else that can be done. I'm not sure if the dealers will do a battery diagnostic like Cincinnati Hybrid.