People have different reasons for where to stay not just on Lemnos but any location.
Staying somewhere that has a good selection of shops, markets and tavernas is important and while I can understand wanting to stay in a village that still has a lot of character which I have done on many trips it comes down to do I have to drive to get to a town that provides those locations and then return?
When I go out to eat I like having a glass or two of wine so I really don't want to drive after drinking.
While Myrina may not be centrally located it does offer a huge selection of options for services. These is an Old Town area that appears to be very nice.
After searching various websites for accommodations I decided that Myrina would be my best option including cost.
I found a nice totally updated and modernized old building on Airbnb on a back street in a Greek neighborhood at a budget friendly price.
Easy to walk all over the town and return to a quiet neighborhood.
On Google maps driving from Myrina to the furthest village (Plaka) on east of the island will take around 47 minutes. Obviously a lot less time to other parts of the island so that will work for me.
I've driven much further distances from where I stayed on the Peloponnese so I'm OK with the driving.
The link that JoLui offered is a great option for accommodations all over the island but check out Airbnb.
As far as renting a car I think it would be mandatory even for just part of your stay.
As always JoLui provides a lot of solid information and the websites provided are great.
There is a lot to see on the island and I doubt buses go everywhere or at convenient times.
Everyone should decide on what's best for them.