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If Mumbai is the financial hub, Pune is well known for its educational institutions and culture and tradition. As the two cities are so close to one another it is but natural that people travel a lot between them.
Traveling between the two cities can be done by road i.e. by hired car or taxi, by state transport bus, or of course your own vehicle. If you want to travel by road you have to take the Mumbai - Pune Expressway. This is a 4 lane highway and very comfortable to drive on. This expressway has made the travel easier compared to olden days when you had to go through what was called the Khandala Ghat which was a steep and narrow pass, through the treacherous Sahyadri Mountains. After the Ghat gets over, there comes a town called Lonavala which is very famous for a sweet food item called Chiki, which is made from nuts and jaggery or sugar. Khandala and Lonavala are the two closest hill stations to Mumbai where people often go on weekend breaks. Lonavala to Pune is a straight flat road. During the monsoon the roads get slippery so one has to be a little careful. The view at this time of the year is simply breathtaking, as one can see many waterfalls cascading down the mountains.
If you are traveling by bus it may take a while longer as the buses make more stops for people to get in or get off at various towns on the way like Vashi, Panvel, Khapoli, Khandala, Lonavala, Talegoan, Pimpri etc. There are state transport buses as well as private bus operators and the ticket charges are fairly reasonable and easily available. There are many pick-up and drop–off points in both the cities and you need to look for the one closest to where you are staying. The travel is pretty comfortable.
There is a train service too. You could either take the inter city trains that halts at Pune station or you could board the local train from CST railway station in Mumbai and disembark at Lonavala station. From here you can change over to the Pune local train which will take you to Pune Shivajinagar station - the heart of the city. Getting into these trains should not be a great problem as the frequency of these trains is good. Pune to Mumbai is a busy route, so if you want a relaxed journey its better to make advance booking.

Flying to Pune is the quickest but a little more expensive option compared to the others. There are daily flights to Pune from Mumbai’s Chhatrapati Shivaji Airport to Pune. The airport is a little away from the city centre but you will always get a transport into town like a taxi or auto rickshaw.