I've done some preliminary, semi-unscientific testing of file sizes with the nano, mainly by making several different videos each lasting one minute (plus/minus one second). The average file size (and thus file size per minute) turns out to be 19.1 Mb (with very little deviation). That means that 1 Gb will hold about 53 minutes of recorded video.
Further extrapolation, from StingerT125's comment: The maximum file size is 2 Gb, so the longest single recording will be approximately 1 hour and 46 minutes.
So, considering that the battery is good for four hours of video playback, you may be able to get two 2 Gb recordings before having to recharge.