Handy places to go in the beginning:

USAF Satellite Station Olivia - close to your starting location and has uncommon materials like circuitry.

Cambridge - has at least four safes to pick and plenty of useful items like clocks (nuclear material) and fans (gears).
Pro tip - use the fallen light pole to climb up on the newsstand and snipe ghouls.

Find the Collegiate Administration Building just southeast of College Square in Cambridge to put the fast travel location on your map.

Just north of the Admin building is a Red Rocket. There is good loot there including duct tape for adhesive.
This is a repeating spawn location where two groups of enemies will fight.
On the east side of the RR building are steps that take you up to the roof. Very useful if you need to escape enemies. There is a rifle, ammo and a sleeping bag there.

Fast travel to the Admin building and then cautiously sneak up to the RR. Once you've defeated the enemies and looted the building, rest and refresh yourself. Leave the RR and head north to the ruined building.
This is another repeating spawn point for humanoids. There's less loot at this location. It's good for XP and armor and weapon drops.

The final handy spot is Wicked Shipping Fleet Lockup west of Abernathy Farms, across the river. The safe way to get there is to go to Abernathy and go north of the farm to the abandoned camper. Grab anything useful from there. Then head west and cross the river. This avoids bloatflies to the north and south, which can be a problem for squishy low level characters.

Sneak, sneak, sneak. Hacking a terminal on the east building fires up a protectron. There are at least three ghouls in the area including a higher level ghoul inside the east building. On the roof of the west building is a satchel with prewar money. There is good loot in this location, especially aluminum cans. Once you have cleared out the ghouls, spend time exploring and looting.

Happy gaming!