What gardens would you recommend us see during our September visit ?
September is not the best time, but Botanical Gardens in Kaisaniemi are open to public and for the open air area there's no fee.
The Winter gardens at the northern end of the Töölönlahti bay.
The Annala villa in the part of Toukola / Arabia has an educational garden. The villa is within walking distance of the Arabia design center and easily reachable by tram and bus from down town.