We did Bangalore - Chennai - Port Blair - Chennai - Bangalore.
This was majorly because the flight tickets from Chennai were way more cheaper than that from Bangalore. And given the connectivity & distance between Bangalore - Chennai, it was not worth paying the difference. This is not always the same, so you might get a better deal from Bangalore at times.
Andaman has a single entry point at Port Blair. Whether you travel by air or by ship you will land at Port Blair and have to leave from here (Atleast if you are doing it legally).
So our round trip inside the islands were planned with first 3 nights at Port Blair, followed by 2 nights at Havelock & another 2 nights at Neil Island. We came back to Port Blair and spent the last night there to finally leave on the 9th day.
All 3 locations on our list were very different from each other.
Port Blair being the capital & the most connected to the main land has most facilities available - markets, ATMs, restaurants & accomodations, public transport etc. The town also works late (upto 21:00 - 22:00 hours) compared to other locations in the list.
Havelock on the other hand is totally focused on tourism & specially around scuba diving. The island is filled with restaurants & accommodations targeted to international tourists. The public transportation here is week but you can hire bicycles & 2-wheeler almost everywhere. The local population here is very small, so they have a small market but it goes dark soon after sunset.
Neil is the least populated place on the list. Its also the smallest island. This place is ideal for nature lovers & peace seekers. You don't have much to do here. There are very limited accommodation & almost no independent restaurants. All you have to do is roam around the beaches till sunset & then enjoy quiet nights in-around your accommodation. But be aware, this was by far the best location for us on both my trips to Andaman.