Hey, In lonavla and lavasa you can book the hotels easily in very affordable prices. Check hotels in the perticular there are very good hotels present. And you should stay atleast lavasa and lonavla so that you can see the sunset at lanava and sunrise in lonavla valley.
You can do a day trip to Lavasa from Pune as accomodation in general is quite expensive there and there is nothing much to do in Lavasa beyond one day. For lonavala there are lot of homestay and reasonable hotels.
I would to like to suggest Lonavala, cause there you will get a hotels as per your budget range. Lavasa is expensive for a stay. better take a day trip to Lavasa. and I would recommend you to stay at Lonavala market area.