Here's what I did.
Flew to Port Blair, took a same day boat to Havelock. Immediately hired a scooty from an agent near the jetty @ Rs 500 per day.
If you want a beachside resort, I highly recommend the east side of the island. Radhanagar beach on the west is nice, but only worth one sunset, not much more.
You can instead spend the entire day chilling at Kala Pathar beach on the east side. The edge of the beach has thick tree cover and beds you can lie down on. There are food stalls nearby that serve good seafood.
In my case I stayed at De Foret which is on the middle of the island. Radhanagar Beach was about 5 mins away and Kala Pathar beach was 20 mins away. Nice pool and food was excellent too.
My first choice was Silver Sands Resort next to Kala Pathar beach but it was slightly over budget. A friend stayed at SeaShell resort and he highly recommended it but it was even more expensive.