Have a free afternoon together? Since the sun has decided to come out and more importantly, stay out, a great way to spend the day is at the Griffith Observatory. It may sound boring, but try as you may; the observatory is anything but boring. The cost is free to get in, which is an added bonus and the time you spend in there is very well spent. You will probably want to allow yourselves a good two and a half to three hours, but some of you may require much more time, which is great too. The only experience that does cost is the Samuel Oschin Planetarium, which I highly recommend. The cost is $7 for those who are 13 and up, or $5 for senior citizens. If you're an LA couple with children, the cost is $3 for kids 5-12 and free for anyone younger. For more information on the Griffith Observatory hours of operation and FAQ's, visit: http://www.griffithobservatory.org/general.html.
Besides the planetarium I recommend heading to both the top and bottom of the observatory. Up top you get some incredible views of this great city we live in. With all the beautiful sights, there are many photo hotspots which you must take advantage. Also, the Zeiss Telescope is located in the dome of the observatory. During the evening hours, the public is welcome to view the sights of the sky through this amazing telescope. 
At the bottom level of the Griffith Observatory, you'll follow a long hallway decorated in nothing but donated "space themed" jewelry. At the end of the hall, you'll find yourself staring at actual meteorites that somehow made their way to Earth. Also, if you're not too timid about your weight, try weighing yourself on each "planet." It's quite interesting and you'll know what I'm talking about once you get there.
The Stellar Emporium gift-shop is also on the bottom level, as well as the "Cafe at the End of the Universe," just in case you get a bit parched or hungry.
With all of the displays and interactive exhibits, the Griffith Observatory is a very original and memorable date for any LA couple. So, enjoy the day and the company (you are on a date) and if the date goes sour, I can guarantee it's not the observatory's fault. :)