With that budget you could probably get a 1b1b pretty much anywhere. If your looking for something new and nice check out the Scott's Collection properties in Scott's Addition by Greystar. They are a bit bougie for me, but you got a pretty nice budget.

I rent from Legend Properties, and have enjoyed them for the most part. They have quite a few properties scattered around the Richmond area and would also be a great choice.

If you do find yourself under budget when you find a place feel free to send some coins my way. Best of luck, and welcome to RVA!