Roaring Camp and Big Trees Railroad in Felton is less than five miles from downtown Santa Cruz...out Highway 9.
The schedule in April is Mon-Fri at 11:00 and Sat & Sun. at 11:00, 12:15, and 2:00
The trains have late 19th century steam locomotives and open-aired and covered passenger cars and travel on narrow gauge rails through the redwoods along a 6 mile, 75 minute trip, These are "second growth redwoods", meaning the area was once logged, but they will still be tall because that was usually done at the turn of the century.
However, on Highway 9 on the outskirts of Felton, coming from Santa Cruz is Henry Cowell Redwoods State Park, where the trees are first growth, I am told. They will be much taller and larger.
There is also a train which leaves the Roaring Camp Station on a round trip excursion into Santa Cruz and the Santa Cruz Beach Boardwalk; however, it only runs May-Oct.
The Boardwalk, however, is a place I would bet your child would love. It has an antique carousel with the original carved horses and it runs to the music of an antique calliope. While most of the rides would be too advanced for a three year old, there is a section especially for toddlers at the far end of the park, with little cars which run on a circular track, and other attractions for wee folk. Caution, it may only be open on weekends in April. Memorial Day is when it begins to be open from 11 to 11 every day. Admission is free you just pay for what you do...ride, eat, etc.
Depending upon the weather, you might want to spend a little time at the beach. Sometimes we get some beautiful days in April.
There are some cottages on Highway 9 near Henry Cowell. I know nothing about them, but they are listed in the Northern California AAA Tour Book and given s two diamond rating. According to the Guide, they have 15 cottages, high speed internet, whirlpool, fishing, badminton, ping-pong, hiking trails, horseshoes and a playground. They have a minimum stay of 2 nights, I believe more in season. Rates are listed as $60-$119 in April. They don't give a website but you might google them to see if they have one. Telephone number is (831) 335-4412.
I would recommend that instead of staying in San Jose and driving back and forth over winding Hwy 17 to see what's here, you stay in this area.
As for places to eat, downtown Santa Cruz has a pretty tree-lined street just full of restaurants, (quite a few with sidewalk tables), boutiques, coffee houses, a 9-plex theatre. One place I have noticed which is very kid friendly is called, no kidding, "Rosie McCann's Irish Pub"...it is upstairs with a largish dining room and they always seem to treat the kids great.
I hope this gives you some ideas. There are lots more things to do in the area....