We have stayed for a weekend in a villa-type building ("Pääsu villa") near the lake with 7-month-old baby. The room ("Õunaõie tuba") had all amenities needed (including baby cot with bed linen) and you can leave a stroller downstairs. The room is well-equipped (TV, hair dryer, small refrigerator, coffee and tea facilities), but no A/C, and you can only open one window, so it could be quite soggy in summer.
Breakfast is included and you can eat outside. There is a small pub where you can buy lunch, coffee, ice cream etc.
Parking free of charge.

You can stay in the 4-floor hostel (a large building), smaller 3-floor villa-type place (some windows are overlooking the lake) and also small houses/cabins designed to fit several families further away from the lake. We stayed in the latter, our unit had its own toilet/shower, porch area, two small beds and a bed under the ceiling (you have to climb the stairs to get there). The bed upstairs was not very clean and there were no pillow cases, but since there were just the two of us maybe that's why they did not prepare it. There is no teapot in the unit (although the website states there is one). Also no hair-dryer. There is a small fridge and a small dated TV. We bought food in Tallinn, so we kept it in the fridge and ate it both indoors and outdoors on the porch. Walls are sound-proof, at least in our house. We had loud neighbors, but as soon as we closed the doors/windows it was fine. There are no curtains on the entrance door. The curtains on both windows do not offer enough protection from the light, so it gets kind of light during summer nights in the room.

Regarding my comment about bed bugs, I was bitten by some insect at night. Although I did not see them, I am 99% sure it was bed bugs, as I was bitten by them before and I have an allergic reaction to them. We were in unit #42. I wrote to the hotel about this issue after we checked out.

Restaurant area (open till 10 pm) is also where you eat breakfast. Dinner food was okay. Breakfast (included in the stay) was not that great: hot items include sausage reminding hot dogs, oats, and omelette, but they are not really hot (more like lukewarm). There is something reminding yogurt there (very sweet), couple of juices, coffee (not that tasty, but hot!), tomatoes and cucumbers, cheese and ham. When we were there, there was also a group of appr. 15 children with accompanying adults, so we tried to get there before them to avoid the craziness. You will not starve, but do not expect anything tasty from breakfast. Breakfast area is very dark, with very non-breakfast paintings on the walls and very cheerful music. Pretty surreal and quite entertaining (but not for everybody).

Administrator at the Reception was very nice. Restaurant staff did not speak much English or Russian, but we still got what we needed.