why not use your smartphone? The only issue would be the battery not lasting too long, but if you can plug it in most of the day, it should be ok.
do you want something like a continuous datalog? or would a location every 5 or 10 minutes be sufficient? the more frequent you want your data points to be, the bigger issue battery life would be....gps receivers use quite a bit of power.
my gf has a garmin forerunner 305 running watch. the battery is supposedly good for ~10 hours, and you can hook it up to a computer to download datapoints.