I downloaded RCT4M a few weeks ago, for free, and I hate to say this, but I'm really enjoying it! Yes, it appears to be free on the app store now, with the only purchases being in-game. I'm playing it on my iPad, so I don't know how it would be to play on an iPod/iPhone.
It's really easy to not have to spend any real cash on the game. You start out with a certain amount of coins and 40 tickets. Make sure you place lots of shops, eateries and hotels to gain lots of money on a daily basis. As aforementioned, there are lots of building time restrictions. My resort took 28 hours to build and my double swinging ship is taking 30+. You can avoid this by spending tickets, but if you have the patience, just wait it out amd save the tickets for other things. That's where I went wrong lol!
The goals are also good fun, and despite sometimes costing you a fair few coins to complete, you get coin and ticket rewards in completion, and also get closer to levelling up. Levelling up equally gifts you free coins and tickets, which is really handy.
So yeah, a nice fun, slightly - but not too - addictive game. Would happily recommend, just don't fall into the trap of spending all your tickets, as they take ages to get back.