Hi Prachi, I have come across a wonderful post on Tripoto about the places you can visit around Mumbai with pictures. You can go through it and plan your trip.
Murud Is an excellent option, however it's a 5 hr drive. alternatively you can use ferry as well. a good beach, great history you can experience everything.
camp temgarh is another option, you can visit lavasa from there.
Daman is also a good option I loved it but opinions can differ. Sunday is a great day to just walk around the fort area in Daman.
or just head to sgnp for a variety of experiences!
If you are traveling by your own car & planning to start your journey on Friday night, ti will give you some extra time to explore. I think going south towards Dapoli, Anjarle seems to be a good plan as this area has a lot to offer. Suvarnadurga Fort, Harnai port, Anjarle, Murud, Karde Beaches.. Even Ladghar is a beautiful place to stay near Dapoli.
Have you heard of Kalvantin and Prabalgad. Its good place for trekking. Its nearby panvel station. All facilities available on top of it. Food, Tent Stay and Much more. Trek is quite exhaustive carry enough water. if you run out of Water it is available and PrabalMachi( Mid Point) you will get everything here, Lunch, Breakfast and Dinner facility.
If you are looking for adventure as well as some leisure time, I have the best option for you..... Check out Bhandardara, dist. Ahmednagar. It's an amazingly beautiful place. It's one of the best place you can visit and chill for 1-2 days. There's mountains all around. Bhandardara is situated in the midst of Sahyadri range. You must visit this place once at least. Check out The Land Of Wanderlust (TLOW) website..... https://thelandofwanderlust.com/