Accommodations near track?

Taxi's and Uber are everywhere in the city. If you book early enough, you should be able to get Air B&B or VRBO

We stayed in an Air B&B less than a mile away.

If you are in NOLA during an event, you can take a taxi anywhere in the city for $4

Define "near". The track is walking distance (about 2 miles) from the French Quarter. Although there are no hotels nearby, there are a number of B&B's along Esplanade that are even closer than the FQ. If you choose to stay in the Quarter or elsewhere, there is also very sporadic bus service or a cab will cost around $10 with tip.