Who didn't love Back to the Future as a kid? The endlessly quoatable movie ("You are my density...") is a favorite, and not just for the nostalgia-- it's supremely entertaining, and it's held up over time... besides, has there ever been a character as cool as Marty McFly? Unfortunately, time travel isn't really an option yet (we still haven't even been able to build a GD hover board yet!!!) but at least you don't need to build a flux capacitor (or acquire large amounts of plutonium) to visit these Back to the Future filming locations.
Your first stop should be to visit the McFly's House, where Marty and his family live at the start of the movie. Then you can hop on your skateboard and head to Doc Brown's Garage, audition for battle of the bands at McCambridge Park's rec center, and test out your DeLorean time machine at Puente Hills Mall, aka Twin Pines Mall, aka Lone Pine Mall. Hill Valley High School, where George and Lorraine, and later on, Marty, attend is actually Whittier High School, and it still looks pretty much the same as it did (plus, Richard Nixon is a real-life alum of the school). The Enchantment Under the Sea dance was actually not filmed at the school's gym... those scenes were shot at the Hollywood United Methodist Church, right in the middle of Hollywood.
Side note: there's also the McFly's House (2015) from Back to the Future II... as unrealistic as their version of the future has turned out to be, I will give them that the McFly house is a pretty decent representation of what homes in 2015 look like. But, I digress. Back to the first movie. Grab some binoculars and peep on Lorraine Baines' House from a tree, just like the awkward George (fun fact, the homeowner of the property with the tree was a small-time documentary producer who released a short little doc on the history of the tree that included some awesome behind the scenes footage). You can also visit Biff Tannen's House and George McFly's House...they're all on the same street in South Pasadena. The adorable town square was filmed mostly at Universal Studios on a set (and it was used in Gremlins as well!) You can see it if you take a tour...it's survived several fires including one sparked by, ironically enough, lightning.
Two houses were used for Doc Brown's 1955 mansion: the interiors were filmed at the stately Robert R. Blacker House, and the exteriors were shot at the Blacker House's "little brother", The Gamble House. Both homes are historic architectural sites designed by Charles and Henry Greene in the early 1900's. Interestingly enough, it's hinted in the movie that the mansion Doc Brown lived in in the 1950's burned down and the land sold to fund his time machine project (perhaps an insurance scam or an experiement gone wrong?)
And if you remember, Lyon Estates was where Marty wound up in the DeLorean after he first traveled back in time. A full-blown subdivision by the 1980's, it was still being developed in the 1950's, one of the first signs of where Marty has traveled in Doc Brown's invention. Art imitates life, and as predicted in the movie, the road is no longer an empty stretch of pavement... business have sprung up along the route. Maybe the movie isn't so unrealistic after all!