Elkwater lake is located beside the town of Elkwater in the Cypress Hills, about an hour SE of Medicine Hat. I stayed overnight in Elkwater on the way back from a work trip a few weeks ago.
Elkwater is mostly a summer village with limited services (pub/bar, a few lodges, campgrounds) but is your best bet for accommodations in the Cypress Hills. I had very dramatic weather while I was there and it was (disappointingly) too cruddy to paddle.
The lake itself looks like it would be nice. It is about 3km east-west and has a northern leg that is maybe 2km long.
There are three easy access points. The first is off the parking lot near the community hall on 3rd Street (above). There is a dock that is silted up and offers a sandy bottom on the east side of the dock.
A bit further west is a public beach and marina. There is a boat launch as well as a nice beach launch. You can also rent boats here. Even further west (Fire Rock campground) there was another boat launch and beach area.
The south side of the lake has a nice walking path and groomed parkland. Despite the bad weather, things were definitely getting crowded with the trailer-and-boat crowd on Friday night. I suspect the lake would be pretty busy with boats on the weekend.
A pretty picture from the next morning (looking west from the causeway) gives a better impression of the lake in nice weather. I would definitely come back here and try again if I was down in the SE corner of the province again.