ReefCI: out on the island there is usually a breeze. I didn’t find the lack of A/C an issue, but once back on the mainland I totally agree....
ReefCI looks really cool. The lack of AC would give me pause, too. I don't really need it during the day but man, it's hard to sleep at night without it (personal experience out in the jungle). Hopefully they have some big box fans.
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Btw, you probably don't want to spend any time more than you have to in Belize City. It's pretty rough, not a tourist town like San Miguel.
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Belize City: second that it isn’t somewhere you want to hang around.