Firstly, you mention being pushed for time. Is it possible that he doesn't want to walk because he is still 2 1/2 which means his legs are a LOT shorter than yours and he can't keep up and/or tires out a lot faster? If he is walking till he is tired and then put into the stroller, it is a bit like getting a really good work-out and not being allowed a cool down or stretch afterwards. That will not feel good for his GROWING musculature. As a preventative measure, only expect him to walk when you can take your time and move along at his pace. Stop and smell the flowers with him, notice the line of ants carrying food back to their nest, and stop to watch the song bird in a tree.
In regard to wanting out of the stroller, I don't like being belted in very much either - I'd imagine that is part of the problem, especially at the age of two.
If you aren't already, you might try making the stroller a funner place to be. Be goofy with him while you walk. Make the stroller "dance." You can make the ride more fun for him by singing songs, making the stroller occasionally go "crazy" by weaving a little or going extra fast and squealing, "Weeee" and being silly about it. Talk about what you see while you walk, tell your son about where it is you are headed and how you will be getting there. Ask him if he sees the lady with the blue hat, the green sign. . . Play games like "eye spy". Choose an object (that's pretty obvious, because he is two) and say, "Hey, I see something yellow, can you guess what it is?" Once he gets the premise let him be the spier sometimes. Then, if you are in a hurry and need to move along he is more likely to enjoy the stroller along the way.
If it is a day when he really needs to be in the stroller, he REALLY DOESN't want to be and is telling you so, you can acknowledge his feelings but still honor your needs. "I know you want out of the stroller. We have to get to X place, I'll get you out there. That'll be about Y minutes from now."
Then, Like Torben says, don't give in. If he fusses you can just repeat, "It'll only be about Y minutes until you can get out." Try to distract him with a little fun or a game that has worked well. Then when you get to the next location, get him out, give him a big hug, and a few minutes to move around before you move on.