Matheran is the closest hill station from Mumbai, and it's quite cheap. One can catch a local train from Mumbai.
And then a mini train to Matheran station or one can get a shared cab which, will cost around Rs 60.
Rooms here are quite cheap, from Rs 500–1500 per night.
My personal advice to all the travellers is don't hire a horse because they are costly plus they won't take you to a majority of places.
Prefer hiking and you will love this place.
Get a navigator and a map.
Discover new places and feel the silence and the beauty of this place.
I had visited 22 places in a day and if I can then you can too.