Can I stay at a hotel at Fort Eustis in VA if my boyfriend is there for AIT training?
Yes but why would you want to? He will be locked up for weeks, and will only be allowed out once or twice. They don't have free passes for nights and weekends.
Of course you can. You can stay at any hotel you want. If he is in basic training, you will not see much of him.
Save your money and go see him when he's finished with basic.