Is there easy public parking nearby for the handicapped?

no not really

There is a municipal parking lot across the street

Municipal parking nearby, last time I went, it was full and I had to circle to find street parking. Give yourself extra time for parking.

Yes, parking next to the restaurant and 2 public ones across the street .

There's public parking across the street

There's a municipal lot across the street that you pay $1/hr but the location also shares a free lot with the Bank of America. When it's banking hours, the lot is for BoA but after hours, you can park at any of the spaces that have the Texas Roadhouse sign. There are handicap spots to the front of that free lot shared with the bank and the sidewalk is right there so you can walk to the sidewalk and around the bank instead of jumping down.

There is a municipal parking lot across the street for a dollar an hour

Yes

Yes right across the street, a municipal parking lot.