Naps at this age are hard for some kids. Both of my kids gave up their naps at 2. I did the whole quiet time thing with my daughter and that resulted in an hour or 2 of me trying to get her to sleep.I settled on taking short drives in the afternoon when I felt like she would melt down. Around 30 months I decided she could just watch an hour of TV everyday. She would zone out and get some rest that way.
My son is now in this fun place. I do the stroller walks or car rides when he really needs a nap, but most days he just needs to go to bed at 6:45. He then sleeps till 7 or 7:30. They need 12-13 hours total. It doesn't matter when they get it, just that they get it. I know many people think little ones need naps, and they do, but sometimes it is easier on everyone involved if the kids get all the sleep at night. Making quiet time work just doesn't work with some kids. They don't want to miss out on the fun and refuse to have quiet time. This is when the TV comes in handy.
A good friend of mine has a 5 year old that naps to the cooking channel every day. It is the only way she has been able to get him to nap since he was 1.
Do what you need to do. I know many people think I am nuts for letting my young 2 year old drop his nap, but the thing is, he doesn't want to nap, and I am not going to fight him. When he really needs a nap, he goes to his room and lays down. Sometimes he sleeps, sometimes he doesn't. I wish he still naps, but he doesn't. I let him watch TV with his sister, and if he is really grumpy, we do the stroller or drive thing. He only got 10 hours of sleep last night, so today I will be doing the stroller or car to make sure he makes up for his lack of sleep.