people have given you good advice and commentary already. how dog friendly is purely relative, i have not lived in the UK but i found europe overall to be more dog friendly than america as a whole, and jersey city slightly less dog friendly than america as a whole but purely because of population density and lack of space (as opposed to social stigma or anything)

there is nowhere you are allowed to have the dog off leash other than dog parks. dog parks themselves are very small, most commonly the size of a 1 bedroom apartment. there are a couple of larger one, i.e. 1/2 an acre etc. you'll obviously not be the only dog

furthermore there are restrictions on the number, type, and size of dogs in high rise apartment buildings. you said 2 but did not specify the size, generally limit is 50lbs. pitbulls and certain other types of sometimes banned. several buildings only allow 1 dog per unit. smaller buildings and individual landlords will have their own specific rules so you'll find more variation and therefore more flexibility if needed

finally dogs are not allowed on the train or subway unless they are transported in a carrier. again it therefore depends on the size of the dog. this restriction therefore makes it impossible to move some dog around without a car, though uber does work