Times Square is one of the most expensive parts of New York City, but it also is one of the most exciting. If you want to enjoy Times Square without having to empty your wallet, you have several options beyond people-watching.
Bring a picnic. If you've never been to Times Square or it's been awhile, you might be surprised to hear that the city has closed off part off Broadway in Times and Herald squares to vehicular traffic. You can sit in the chairs at the tables that are now part of the pedestrian area and have a picnic. Times Square gives you the chance to spend a day relaxing for free and enjoying a nice lunch in the middle of one of the busiest places on Earth.
Check out the lobby of the Marriott Marquis in New York Times Square. It has an amazingly tall atrium and offers a nice place to enjoy a drink or take in the sights for the afternoon. You don't have to be a guest or spend any money to look around the lobby or ride in the glass elevators that zip up and down the middle of the enormous atrium.
Check out the TKTS booth in the middle of Times Square. It offers deeply discounted, same-day tickets to Broadway plays. This might be ideal for someone wanting to see a play but without any particular preference.
Go to B.B. King Blues Club and Grill on 42nd Street for free music in Lucille's every night. Lucille's is a separate area inside and gets its name from King's guitar.