http://parklaneequestrian.com/academy/
This used to be the place that I would rent a horse and ride sometimes ... rarely, but it's very centrally located in Dallas. My experience with the place was decades ago.
Now, they've turned this property into an special event location but I bet that they still offer riding. It's worth a try because of the location.
Otherwise, everyone will suggest Poontang Alley (The Galleria area) for a place to stay. However, I would be inclined towards staying close to downtown. Perhaps off of Market Street.
It's very centrally located and it's just off of the I35, which is convenient to a lot of people.
However, I'll freely admit to not following the others for the most part!
Good luck,
Elisabeth