No need to stop at both, and with just one afternoon, you probably don't have time for both. When will you be here? Although Henry Cowell is closer to Santa Cruz, this time of year more is open at Big Basin, and you will be able to see more trees, and nice walks.
As far as lunch in town, there are many nice places. What type of food do you like? If that's not really a concern, I like lunch on the wharf. There are several restaraunts available with nice views. There is parking right on the wharf and you can look at the menues posted by the doors.
Lunch: Get something unique, go to Charlie Hong Kong. It's kind of Asian street food fusion. Seriously, I would go here; it's by the morrisey exit. From there it's a drive down the street to Seabright beach.
Haven't been to either park in a while, but if you have limited time go to Henry Cowell - Big Basin is way out in the cuts while HC is more central (more - still not very central).
Depends what you want to see. If you are going to commune with big redwood trees, Henry Cowell is the place. The one mile flat redwood loop is magical. You will see more giants in one place than anywhere on the central coast. If you want to do more long hikes, Big Basin has that over Henry Cowell.
As far as lunch: I would recommend Malabar Restaurant on Front Street for the most amazing Asian Fusion cuisine, unless you are there on a Sunday. Malabar is closed for Sunday lunch. On Sunday I'd try Center Street Grill (The Kitchen Fave pizza or Chinese Chicken salad) or Cafe Limelight on Cedar St. (Faruk's hummus plate).
If your daughter is a people watcher you might enjoy lunch at either the Cafe Delmarette or Hoffmans, both on Pacific Ave. in the heart of downtown. Both have wonderful food and seating up by the sidewalk where you can watch the parade of humanity go by.
In July, Henry Cowell will be your best option.
Charlie Hong Kong is a great idea for lunch! Not much of a view though.
I agree that for your purposes, Henry Cowell Redwoods works better than Big Basin.
Henry Cowell is only 7 miles up Hwy 9 towards Felton from the intersection of Hwy 1 and Hwy 9 in Santa Cruz.
Big Basin requires a trip of 13 miles up Hwy 9 to Boulder Creek, then a 17 mile loop through the park. From here to San Francisco without backtracking, you go on to Saratoga over some winding roads and end up near Hwy 85, then to 280 and on into the city.
If you are planning to drive to San Francisco all the way on Highway 1 you only have to backtrack 7 miles from Henry Cowell. If not, take Mt. Hermon Road from Felton over to Hwy 17. After the trip over the hill and after Los Gatos, take the Hwy 85 exit north and then Hwy 280 to San Francisco. This is a pretty and uncrowded freeway which goes through the foothills of the Coast Range.
I also agree that Pacific Avenue is the best place for lunch. It is a lovely tree-lined street packed with sidewalk cafes, boutiques and bookstores. The cafes mentioned are good, but if it were I, I would stroll the length of the street and pick out what appeals to you. They all post menus.
Watch out for the boutiques, which fascinate teen girls, especially Urban Outfitters, if she is familiar with that one. <smile>
Here is a Traveler's Article about Santa Cruz which mentions some other things you might want to see or do while you are here.
Have a wonderful trip.Edited: 21 February 2011, 17:47
Kyhber Pass is on the 'interesting' side of downtown, the food is good and you will get a nice cross-section of people there but it might be the seedier crowd. The Palomar Taco Bar is an excellent place to get lunch for cheap and, while indoors, has a lot of people wandering through. Zoccoli's is good but doesn't have as much foot traffic. Whatever you do wander up and down Pacific Avenue afterward, Santa Cruz has lots of colorful characters and you can usually buy art for a nickel if the right guys are out.
The Crow's Nest upstairs is the place to go. A nice outdoor patio overlooking the bay and harbor. Great salad bar, and lots of choices.