Local buses cheap, good and efficient. No underground.
Moldovan currency is probably together with Belorussian and Ukranian one of the less worthy in Europe. 1€ is about 20moldovan lei, you have 1leu banknote... Better busk in Romania or euro zone and go there to spend, still it may works in the city centre.
Located in the very centre, inside a huge beautiful almost abandoned place, "Art Labyrinth" (http://www.art-labyrinth.org/en) is definitely "the" place you must visit and know in Chisinau (which can actually open you to many other places and people). Calm, relaxed and very easy going, the guys will welcome you with very good teas, jam sessions with hangpans or drums and very good atmosphere. If you have a broken instrument, they might also know somebody fixing it completely for free, just for a great smile..
If you have the chance visit also the eco-community "Chaslieva" (happiness), lost in the hills some 60 km north of the city, at art labyrinth they can have some contacts.