A few comments about Santa Cruz.
1) The Boardwalk is basically an amusement park with free admission. The rides and arcade games are only open on the weekends that time of year. If you are looking for a beach, Natural Bridges is only a mile or two away and much more impressive and enjoyable. The Santa Cruz wharf adjacent to the Boardwalk is worth a stop for lunch. Try Gilda's for good basic food, reasonable prices, and great views.
2) The best and easiest places to see the redwoods are not directly adjacent to the beach. Your best options are Henry Cowell Redwoods State Park going in at the main entrance off highway 9 just south of Felton (paid admission) or the campus of the University of California.