Nikon recently released newer models to replace the now discontinued D3000 and D5000 (the D3100 and the D5100 respectively).
I would say either is a GREAT camera to get for a beginner. The D3100 is more "hold you hand through it" than the D5100, but at the cost of a better sensor and less features. If you can shell out the extra 300 bucks for the D5100, I'd say go for it, but if not..you will NOT be disappointed with the D3100. I would say stay away from the older models as Nikon is flushing out all the older models for the new...and seeing how most people don't buy a new DSLR every year, you'd want one thats at least "new" that will be the current model for the next few years.
Just to give you a quick list of the advantages of the D5100 over the D3100 (again..both are GREAT cameras..so don't see this as a bash on the lower model).
Better low light sensor on the D5100 (good for dark rides and nighttime)
AEB (or auto bracketing) on the D5100 (if you eventually want to dive into HDR photography...plus the D5100 has an "auto HDR" function)
Better build quality on the D5100 (a little bit heavier too..which some may see as a negative)
Swivel Screen on the D5100 (comes in handy more than you realize)
Better video control and output on the D5100 (tho the video on the D3100 is fantastic at 720 24fps)
Faster autofocus on the D5100 (but not by THAT much)
External Mic input on the D5100 (in case you eventually want to go that route for video recordings)
Built in camera effects (which are neat to play with and easy for a beginner to utilize)
That being said, the D3100 isn't without its advantages as well..
First off..cost. Its 300 bucks cheaper. Which can be spent on new lenses (may I suggest a 35mm 1.8 or the new 50mm 1.8..both are amazing..and inexpensive)
Second...The "guide" function. It's a great learning tool only available on the D3100. You say what kind of picture you want to take, and it sets it up for you, and tells you how to do it yourself manually next time.
Now I don't personally have a D5100 (it just came out last month) but I do own a D3100 and the higher D7000, and I just always bring the 3100 with me to parks (less expensive so I don't worry about it AS much as I would the much more expensive higher model). So I can tell you first hand that it works fine for theme parks...
<a href="http://www.flickr.com/photos/dreggs/5547635058/" title="DSC_1020.jpg by DreGGs, on Flickr"><img src="http://farm6.static.flickr.com/5055/5547635058_381b9606c9.jpg" width="333" height="500" alt="DSC_1020.jpg"></a>
<a href="http://www.flickr.com/photos/dreggs/5547068849/" title="DSC_1277.jpg by DreGGs, on Flickr"><img src="http://farm6.static.flickr.com/5092/5547068849_7cb518d532.jpg" width="500" height="333" alt="DSC_1277.jpg"></a>
<a href="http://www.flickr.com/photos/dreggs/5547650640/" title="DSC_1285.jpg by DreGGs, on Flickr"><img src="http://farm6.static.flickr.com/5135/5547650640_b788cffd81.jpg" width="500" height="333" alt="DSC_1285.jpg"></a>
All taken with my D3100.