Just in town, 1 km from the Old Town is Park Kadriorg, where is nice palace Kadriorg with the nice garden and art museum inside. It is big park for walking, there you can find a few ponds and fountains and also Estonian presidential palace is located there.
If to go out from town then I would recommend to visit Lahemaa National Park and go to “Viru bog”.
Lahemaa represents many faces of Estonian nature; some bogs (like Viru bog), some pristine forests (around Oandu) and beautiful sea-side views (for example in Altja and Käsmu).
There are a few providers offering day trips to Lahemaa from Tallinn, but you can also just rent a car yourself and explore the area. In that case, you can start at the visitor center at Palmse and ask what places are particularly worth a visit at that time.
Lahemaa has my vote, too. One thing - have mosquito repellent with you. You will need it in July.