is there parking close by?

Yes. You can park across the street from the museum.

The above answers are great. There is also a smaller parking garage about 2 blocks west of the museum on the same street. It's easy to miss and i found it by accident. You pay with a credit or debit card near the entrance and place a receipt on your dashboard. The cost varies based on how many hours you choose.

There's entrance to parking garage on Commerce st and one on rear,across from Briscoe Museum,on Market st.

There is a parking facility on Market Street opposite the museum. I believe the entrance to the parking is actually on Commerce.