of the two places you asked about, i'd recommend staying in placencia. hopkins is a village with much more limited resources for the visitor. some people prefer a less developed atmosphere but for what you want to do, access is easier and there are more choices available in the placencia area.
if you want a resort diving course, i think robert's grove can provide that and i don't think you have to stay there to take lessons. monkey river trips leave from placencia regularly, the various tour companies put out chalkboard signs with their next day activities so you can just stroll the village and see what's up and make plans for the next day. or have someone from your hotel call for your reservation. you have access to lots of conveniences like relatively well stocked grocery stores, internet cafe/shop, BTL office, small souvenier etc. shops, a wide selection of accomodations in all ranges of price & fanciness, lovely beaches and the best ice cream (gelato) shop in belize. there is also a slight chance of some nightlife in placencia---ask around to find out if a band will be playing anytime while you are there.
both hopkins and placencia are very quiet, laid back locations, hopkins is just the quieter of the two by far. placencia has a little more to offer, in my opinion.
if you leave from san ignacio by about 7/7:30 AM on the bus, you can be in placencia just after noon, seeing a lot along the way. you can also just bus to dangriga, cab to the airport and fly the rest of the way to placencia and be there by mid- morning. i have done the bus from san ignacio to placencia several times and it's a snap. to get back to belize city, fly from placencia to goldson airport and you can plan to be there right when you need to be for check-in.
try not to stress out too much---i think windwalker's idea is a good one and it would take a lot of pressure off your schedule.