Liverpool and Snowdonia by car

Visiting Liverpool by car and staying at a hotel near the airport (both
choices due to cost). Is it (financially) feasible to park in the city
centre in the evening, and if so, where? Or would we be better taking
public transport or a cab? There's 3 of us.

During the visit we intend to drive to the northern part of Snowdonia
National Park for a day trip. Any suggestions on where to go for the
best views and a chance to stretch our legs for a while (has to be easy
terrain, though).

A pointer to a good pub for lunch would also be much appreciated.

All this takes place here in February.