I don't usually take cabs around here so I can't recommend one. There aren't many though.
I'm not familiar with the #249 bus - but the #246 has stops in several places in the Clear Lake/JSC area. You aren't planning to walk from your hotel to JSC, are you? I assume someone is picking you up at the main gate because without a badge you aren't getting past that. Could that person give you a ride to the airport? Or from your hotel to JSC at least? Walking from your hotel to JSC will take longer than 30 minutes I think. What if it rains?
An economy car could work out much cheaper than cabs - I'd look into it at least.