Note the word should. 1801 Winscott Road, 249-0770. It's affiliated with nearby Benbrook Driving Range. Longest hole is 177 yards. Longest hole is about 165 yards.
Every facility mentioned above has some sort of putting green.
You generally don't need a tee time at a par-3 course, and you can take your chances visiting a regular course without a reservation. But reserving a tee time is recommended. You might not get exactly what you want, but you should get something close. It's a good idea to call at least three days in advance, but most courses won't take tee times more than seven days in advance. Fort Worth municipal courses recently began using a computerized system.