Alibag is very accessible by bombay and is a great weekend gateway!! But remember, there is not much to do around there except going to the beaches and the fort.. of course u can b really adventurous and go upto murud fort and beach!!
the best way to get to alibag is by sea.. the ferry costs around 80 rupees and takes around 1 1/2 hr while the catamaran takes 45 mins and costs 110 per person. this link has the timetables and the contact numbers of all the ferry and catamaran operators - https://raigad.nic.in/HTMLDocs/transportation.htm
once u get there, the better option is to take an auto instead of the bus which is usually too crowded. If you are a foodie.. DO NOT MISS SANMAAN!! amazing food and amazing place!!!
I wud suggest that u go in for a resort like big splash which is both affordable and high on service!! STRICTLY AVOID SUN - N - SEA!!!!!!