Well, nobody can really predict what the weather will be in June during your visit, but statistics are on your side. Scattered showers interspersed with lots of sunshine is fairly typical summer weather, and exactly what my husband and I experienced in July 2006 for our first visit.
Grenada is a good island for vacationing on a budget because it really does offer a generous range of accommodations for well under US $100/night. Giving us more specific information about your budget as well as what you & your daughters seek in a vacation will be extremely helpful.
As the previous poster pointed out, you can find a fantastic deal for the LAE Cottages via SkyAuction.com, a reputable auction site. Just make sure you read the fine print and know what is included with the auction as well as what the additional DAILY taxes and service charges are.
Check out www.GrenadaExplorer.com for a nice listing of accommodations. LAE Cottages are self-catering and thus can help you save a bit of money by preparing breakfasts and other snacks/meals at "home." It's also right on a nice but smallish beach called Prickly Bay.
In a similar price range but with fewer ameneties, check out the Coral Cottages, also in the LAE area. (It stands for Lanse Aux Epines and it's the name for a largely residential peninsula along the south coast.)
Hideaway Apartments is right on the water, a short walk away from Grand Anse Beach. They offer both a garden view and sea front apartment there. Right on the bus route, for easy shopping and going back & forth.
If you could spend a bit more money, there's a villa called Gardenia Cottage in the LAE area. Three bedrooms, your own small pool, water views from the verandah on the roof, and only US $950/week.
The Caribbean Cottage Club could also work for you in your budget, but it's a hillside placement with views to the water, not actually on the water. Restaurant on site.
There are some new suites being built right now called the Spice Tree suites, run by Anthon and Sharon Antoine, in the LAE area, within walking distance of Prickly Bay beach. I'll be staying there myself next month and they gave me a good introductory/previous guest rate, but I think the rack rate there is US $95/night. Full kitchen facilities, both one and two bedroom apartments, and I think the owners mentioned they were working on putting in a pool.
Let's see, where else? Caribbean Breeze apartments, Maitland's apartments are all in a good price range. For a little bit more, take a look at Blue Horizons, across the road from Grand Anse beach and with charging privileges at the tony Spice Island Beach Resort.
Want to stay right on the beach? Take a look a Flamboyant and Jenny's Place on Grand Anse, or La Sagesse on the south east coast in a very beautiful but very secluded location.
Grenada is a wonderful place to stay and is quickly becoming my favorite island to visit.