We visited during A school and also went for graduation.  I agree with mayawolf that staying on/by the base would be most convenient.  Since you are going for your birthday, you might want to check out the Hotel Emma and stay in the Pearl district.  It’s at the “arts” end of the Riverwalk and is a very cool place to hang out and has some great dining.  They have hotel specials all the time too so definitely ask.  Our son really enjoyed hanging out with us there, it was a nice break from being on base all the time.  I think it was about a 15 minute drive to the base from there if I remember correctly.  

I'll give an update in about 2 weeks as we leave this coming Saturday for San Antonio for our son's graduation.  His graduation is 4/25.   We haven't seen him since January 2.   Can't wait.  We will be there for a full week.   And we are hoping to see him just about every evening.  I will send you a friends request on here.