If you just want data for experimental purposes, the VAST Challenge dataset from 2011 has geolocated tweets. Specifically, the data for mini-challenge #1 (follow the MC1 Materials link) has the tweets. Please note the request to register in order to download the data.
Note that the coordinates in this dataset have been fabricated such that they're contained to an area roughly 150 square miles. The messages have been cleaned to remove actual names, and include some "fake" messages specific to the VAST challenge (messages indicating someone is sick). However, it is good for research and experimentation with geo-located tweets.