Fair Hill Park in Maryland is excellent for horseback riding. The trials are endless and amazingly kept and marked. The management and pedestrians are very plesant and they have trails, fields, jumps, and water to cater to any type of rider.
Also, it is available to rent stalls and park trails and I think rv's or tents that you can tack up and ride from.
You could go to the state websites, and then to their department of natural rescources or department of wildlife. They should have listed there the state run parks & trails with all the info. The state ones are usually very well kept and clean. Have fun