Summer is the slow season in Belize, so the accommodation rates will be lower. In Placencia, you can probably score a beachfront cabana for $60 to $75 a night. I know it's good to have everything in place before you go, but the best way to drive the price down probably even lower is to show up and negotiate in person with cash in hand. But for a first-timer, that might be more trouble than its worth as you'll definitely want to have a place lined up for at least the first night. You can get one with a kitchen and save some money on eating, too.
I know that Splash can make suggestions on places to stay within your budget.
Since there are two of you, it may also be cheaper to rent a car and drive to Placencia rather than fly. I haven't checked airfare recently but it seems like it goes up every year. Again, as a first-timer you may prefer just to fly but the drive is easy with just a couple of turns (take a left out of the airport onto the Northern Highway, then a left to get onto the road to Hattieville, then another left at Belmopan, up and over the Maya Mountains on the Hummingbird Highway, then a right onto the Southern Highway and a left at the roundabout onto the peninsula and into the village, all well-marked with signs). It just takes a couple of hours and is a beautiful drive, especially the Hummingbird with its one-lane bridges. I always use Placencia Car Rental, which provides cars at both the airport and Placencia. The drive is about 2.5 hours versus 30 minutes by air. There are advantages and disadvantages to both.
One other tip, the BZ Dollar is tied to the US Dollar at $2BZ to $1USD. So posted prices can seem very high. Always clarify whether the price is BZ or US for whatever you're buying. And US money is widely accepted, actually preferred, but make sure there are no torn bills as they won't take those. Change back is often in Belize bills so I take lots of $5 and $10 bills with me when I go to avoid getting stuck with too many Belize dollars at the end.
I don't mean to sound like a shill for Placencia. I love it there but it's not for everyone. AC has more of everything, i.e., hotels, dive shops, restaurants, bars, etc, but with that also comes more crowds. Placencia up until relatively recently was just a sleepy fishing village and it still retains a lot of that character. It has the added advantage of quick and easy trips on the mainland but the disadvantage of longer trips to the reef. I love running around in the jungle as well as riding around in a boat so I don't mind that at all but it's a deal breaker for some.
Wherever you go, you'll have a great time.