Melville is a big mix - there is a very large commercial business district called the 110 corridor which runs a large length of the town which is Huntington Town - I worked in Melville but really don't know too much about living there - my guess it is pretty busy and not too peaceful - 110 has really bad traffic with all the business and malls and every type of store you can name. Convenient for sure for shopping, but not quiet.
However, not sure of your budget but probably the nicest area south of 25, Jericho turnpike (also very trafficked) Is the area off 25 (not 25a) on Sweet Hollow road. It is surrounded by West Hills Park which is beautiful and when you go up that road you feel like you went back 50 years on the Island and you are 5-10 minutes from Melville and the LIE. I commuted on that road to avoid 110 and also to have a nice ride before work. If not then the Huntington, Northport areas north and near 25a are very nice, and probably a little pricier than some areas, but if your thinking Garden City then those areas shouldn't be a problem. South Huntington is also very nice and convenient to town and amenities and some fun as well.
Also if you are thinking Melville then you can go south on the Island as well, I am not really that familiar with the south shore though.
I guess it comes down to how much you want to commute which is measured in time - not distance. For instance to go from Huntington to Melville near the LIE on 110 could take me 45 minutes to go 9 miles. some thing to think about. Not on Sweet Hollow though only took 15
Also known as "Zombie road" because it twists and turns and only room for one car esp in snow.
Good luck you will probably get a lot of help here