There are quite a few beaches within an hour and a half drive from Halifax harbour, both east and south along the Atlantic coasts of the province. Some have picnic facilities, toilets and canteens. Some are hugely popular and generally always crowded and some are a bit further away but worth the drive. Most have supervised areas in summer. None of them are going to have warm water. This is the North Atlantic but by August you won't go blue quite so fast. You may, however, make the trip on a hot sunny day from the city to find fog at the beach.
Cole Harbour (turn off Cole Harbour Road at Bissett Road, Dartmouth): Rainbow Haven, has boardwalks, facilities, tends towards families and younger people.
Go a little further down the same road and you will reach Lawrencetown beach. Popular with surfers. MacDonald House on the top of the hill before the beach has a nice little tea room. Beach is rocky, unless the tide is out. Supervised areas, canteen, toilets, boardwalks, parking.
Further along the 107 east:
Martinique Beach and bird sanctuary. It's a provincial park and wooded and has open picnic areas. Long sandy beach, really nice and worth the drive. Near Musquodoboit Harbour, down East Petpeswick road. My personal favourite.
Clam Harbour. Huge sand castle contest here every year in August. Thousands of spectators come to see it. Long beach, supervised on weekends, toilets and shower facilities. Turn right at Lake Charlotte. 50 miles from Halifax so a good hour or more drive.
South from Halifax:
Crystal Crescent: three beaches, the third one (farthest) is clothing-optional. Hiking trails nearby, not many facilities. Sambro, NS
Queensland, near Hubbards (exit 6 off hwy 103), is probably the most popular but it's very small and personally, I would drive a little further and go to Bayswater beach near Blandford at Hwy 103, exit 7 to the 329.