Tintagel itself is a village (quite gift-shop-y) and so is fine with a back carrier unless you're over 6ft then the low older-building doorways are going to be an issue of course, but that's the same anywhere. Tintagel has a couple of main attractions. The Old Post Office is one, it is in the village itself, as long as you take your back carrier off for the duration you will carry baby around it Ok. Tintagel castle though is accessed by steps. They are steeper than a domestic flight of stairs, uneven in depth (although English Heritage have made them fairly safe) and very high. I would think twice about taking a baby up there in a carrier, although other people do it. You can decide for yourself though as there is a cafe at the bottom of the steps and to get to the cafe it's a normal steep hill downwards from the village, so even urban-type buggies would be alright that far.
On the way to Tintagel/ back from Tintagel I recommend a stop in Boscastle as the two villages compliment each other for one day out together. Boscastle has The Museam of Witchcraft which is both fascinating, creepy and moving. You will have to carry baby in your arms though as the building is small, old and pushchairs or back carriers wont really work, so I leave it to you to decide if it's worth it. None of the exhibits are likely to scare a little baby, it tends to be grown ups who read the scare into them.
Trebah gardens in on the river Fal, about 2 hours drive away from Padstow. It's nice and everything, but why travel that far? Prideaux Place gardens are actually in Padstow and open to the public, or for more of a whole day out there is Lanhydrock (National Trust) about half an hour away, which is a big house and garden.
Fancy a farm park? Old McDonalds farm is close enough, just head down the Pasdtow-Newquay coast road and after Porthcothan (you wont miss Porthcothan) you will see the signs.
A bit further along in Newquay is an Aquarium, which like the farm park is very baby accessible.
Someone mentioned cycling the Camel Trail. There is an abundance of bike hire places and it's easy to find bikes with baby carriers. The scenary is gorgeous and the trail is pretty flat. You can also walk the trail with a pushchair or back carrier if you rather, it's not just for cycling. 5-6 miles along from Padstow is Wadebridge, with lovely boutique shops and a nice park to unwind in (with trees and benches but also with swings and slides).
For the wildcard half-day out when you're alone with baby try Trevathan pick your own fruit farm and St Endellion. My 9 month and I old love it there. After picking fruit sit down in the conservatory or outside for a cream tea with a view to die for before meeting the goats and rabbits and playing on the swings and in the sandpit.
Best beach for tiny ones? I'd use Polzeath, Daymer Bay or Porthcothan in that order. You will need car park change.
In all, North Cornwall is lovely for a baby, even on your own, and you wont be short of places to go or ways to relax. You do really need a car though.