Here are a couple of things that may be unique to LA.... At the base of Santa Monica pier in the late morning or afternoon (late afternoon recommended) rent bikes (or trikes) and ride south to Washington Blvd.
http://www.nearfield.com/~dan/sports/bike/beach/southbay/index.htm Although experienced riders with decent equipment could vector onto Washington Blvd to rejoin PCH to Redondo Beach and eventually ride the Palos Verdes Peninsula through Portugese bend I would NOT recommend that for the average out of town leisure rider. And allow a little time to pause to stretch, look, possibly get a quick snack or to snap some photos along the way. On returning to the base of SM pier - grab lunch or diner near by. If near dinner time - get a restuarant with a view OR return after dinner to stroll the pier and enjoy the sunset from the pier or area surrounding it. THEN in the evening hop a few of the rides and/or stroll through santa monica place (2 blocks away) and dance an Argentinean Tango lesson in the promenade or look on as most folks do at that plus all the other varied street acts. OR - get your dinner from one of the cafes/restuarants along the Santa Monica place and people watch over a slow meal. IE, get a decent table with a view.
Another idea... if the season fits the schedule.... go in for an early dinner in or near Hollywood OR - order a take out meal, bring a bottle of wine and picnic by the Hollywood Bowl. Then go in for the evening concert. Either get really really nice seats (boxes only) OR really cheap seats and sit where they have not sold a better section out! IE, buy $1-6 seats and sit just behind the sold portion of the lowest section you can get into. Typically on a thursday this can mean any section just behind the asile dividing the terrace boxes and benches. Last nite I took my parents to "The American Songbook"... jazz Vocalists primarily - and my father remarked that it had been the best concert he had seen at the Bowl in half a decade! My tickets were $1 each bought long ago - and we sat about row 7 behind the terrace boxes OFF CENTER. Oh yeah - off center close to the main entrance side there was NOISE from the snack and restuarant concession ventalation of their kitchen areas. I would recommend sitting either further back or more towards center - again requiring you sit further back to minimize or elimenate the faintly distracting noise. Last nite the rear most sections of the Bowl were sold out solid but when you got in they were 99.5% empty as EVERYBODY had spread out into the empty sections below! OH YEAH... if you want to bring liquor into the bowl - it cannot be in GLASS containors. I've heard of premium wines now packed into paper or soft boxes... I can't recall who makes it or weather it qualifies as anything memorable to indulge in. AND ... after the Bowl ... wander the town for late nite coffee or desserts. That might mean - who knows what and where - but you're bound to find something between 10:30 and midnite. I'll not spoil the "adventure" of this stage with any specific suggestions - except to say try driving down Melrose towards Beverly, then turn south on any major street. If you find nothing hen dog west on Santa Monica or Whilshire and zig north on another major street to say Melrose or SUNSET and then dog west again. You really ought to find someplace for a nice cup or coffee and / or dessert to muse ove the evenings performance.
A 3rd thing to do .... HIT
DIsneyland when it opens on a THURSDAY... and try to ride EVERY SINGLE ATTRACTION in a day. Pack some heavy snacks going in so you don't have to take significant time off a ride or line for food. And this should occupy your sense or urgency for fun for the day! Or rather... it should leave you with days of silly egar anticipation for days or weeks preceeding the visit. IF NOT, then this might not be the right diversion for you. AND if it does occupy your imagination for days or weeks before the visit - then it SHOULD give you something to muse over for some time AFTER the ernest attempt! I suspect if you bring your kids along they will be convinced their parents had finally "lost it". Plan it on paper and you'll see that you actually have to RUN to make time to actually be serious about this. That is... if you actually think it's possible in a day!
And 4th.... As an alternative to #2 above.... catch a large stage production from the Pantages (above left) theater - or a small stage production form the
intimate Mark Taper Forum (above right) ... or LA Phil at the Walt Disney Concert Hall. The Mark Taper has a "HOT TIX" line tat forms about an hour before perfoemance - or earlier for popular shows and these are unsold tix for $!0 cash sold 15 minutes or so before curtain.
Hope this helps....