I haven't committed on where I'd day trip from (Nazare or Lisbon) but the frequency and train give Lisbon the advantage. I prefer trains as they come more often but I am reading RS guidebook and sometimes he recommends the bus over the train in certain circumstances (too many connections, not directly on train system) I'd avoid the weekends for these 3 destinations and will not be renting a car on vacation.
Óbidos is 1 hour bus ride from either Lisbon/Nazare (more frequent from Lisbon), tour group I've read that the crowds begin at 930am, peak 11am-2pm and things calm down after 5pm
Tomar is a 2 hour train ride from Lisbon (more frequent that bus from Lisbon or Nazare) and 2 hour bus ride from either Lisbon or Nazare, I was planning on arriving no later than 930/10am and heading back after 5/6pm.
Evora is an 1 and a half on bus (more frequent) or train from Lisbon.
I realize I would be losing a bit of time by day tripping and not spending the night but it is so comforting not having to repack and resettle every day or every other day.