Pompeii is definitely not buggy friendly, you would need a sling. The ground is so uneven in places I wouldn't even want to walk around with a baby in a sling in case I tripped.
Sorrento is flat but there is a steep slope down to the harbour. The streets are very busy and the pavements very narrow so it would be difficult to walk around with a buggy unless you are in a pedestrianised area. Also, there is nowhere to walk along the front as it is built up right to the cliff edge - mainly with hotels.
I think there are far more baby friendly places to stay in Italy than the Sorrento peninsula.
You won't get a buggy around Pompeii easily , all the streets are large uneven stone slabs and steps, and it is vast to walk around with little shade. The towns on Amalfi coast tend to be on a steep gradient although Amalfi itself looked large enough that some was more level and it had a proper seafront.
Do-able in a sling but not a buggy. You will get exhausted though if you try and do the whole site - it's HUGE. Very little shelter or refreshments there too, so dress appropriately, take lots of water and snacks. The Amalfi coast is lovely. The villages are steep, but most are centered around a square where things will be relatively flat with cafes etc. We stayed in Sorrento which is lovely and has some surprising tucked away places if you wander from the main square. Capri is also a trip worth taking. There are local buses and a small train from Sorrento to Naples to help get around. Naples is dodgy though and full of killer mopeds, so mind how you go there. You will definately need a sling though.
I'm planning our October Italy holiday, and was hoping someone out there can tell me if Pompeii is 'do-able' with a 4 mo? Also how about the Amalfi coast? Are the villages/towns just too steep for a buggy and/or lugging my boy around in a sling? Any hotel or villa recommendations are very welcome!