In 1913, the Lincoln Highway Association was formed to develop a coast to coast highway, from Times Square New York City to the Golden Gate in San Francisco. They did a good job providing sign posts along the route, but never raised enough money to pave more than a small portion of the route. In 1925, the Federal Government decided to use the Lincoln Highway for much of its US Route 30. From Philadelphia to Grand Island Nebraska, US 30 was the Lincoln Highway. West of Grand Island, Route 30 goes north-west through Idaho, to Portland Oregon. The Lincoln highway continues due west, through Salt Lake City and Reno Nevada.
Ever since the mid 1970s, the Lincoln Highway has been superseded by Interstate 80, west of north-eastern Ohio. Nebraska still maintains a separate Route 30, but most of the other states just moved US Route 30 onto Interstate 80 and downgraded the old Lincoln highway as a two lane local road. Some portions of the road still maintain the signs of the old Lincoln Highway and call it a "historic bi-way".
There are several books about the Lincoln Highway, that show photos of the road side attractions with old post-cards. These books will give you an idea what driving coast to coast would be like in 1933.
"Greetings from the Lincoln Highway: America's first Coast to Coast Road" by Brian Butko (2005) which is out of print.
"The Lincoln Highway: Coast to Coast from Times Square to the Golden Gate" by Michael Wallis and Michael Williamson (2011)

No less a figure than author Scott F. Fitzgerald took a road trip from Conneticut to Alabama in the summer of 1920, with his newlywed wife Zelda. Scott's account of their journey was published several years later as The Cruise of the Rolling Junk.

As the title suggests, one of the challenges of long-distance automobile travel in the 1920s was not just the condition of the roads, but the vehicles themselves. This was the days of white-wall tires, which were more similar in their construction (and durability!) to a bicycle tire than to a modern steel-belted radial. Any trip of more than a one or two hundred miles was almost guaranteed to involve at least one flat tire. Modern travelers take for granted that it's possible to travel thousands of miles without needing to change a tire.

Another interesting early road-trip book was Across America by Motor-Cycleby by C.K. Shepherd. Paper copies of this are now quite hard to find, but it's in the public domain now, and can be found on Archive.org. Shepard was an ex-RAF officer who rode an Indian (the brand) motorcycle across the United States in 1919, and reads like a cross between Bill Bryson and Bertie Wooster. A constant theme in the books is the poor condition of the roads outside of a few of the major Eastern cities. Shepard's goal was ostensibly to see the Grand Canyon, but he admits that he's doing it for the adventure, and that a more sensible person with his level of resources would have bought a train ticket San Francisco and then hired a car and driver.

I can't answer for 1933 specifically, but to build on /u/davratta's answer with respect to the Lincoln Highway, you might be interested in reading about the Transcontinental Motor Convoy undertaken in 1919. Interestingly, this features a young Dwight D. Eisenhower! He was a 29-year old lieutenant colonel at the time, and part of the 200+ men and 80 trucks that formed the convoy. The trip was meant to raise public awareness of the poor state of America's transcontinental road system and give Army officers and drivers experience running big convoys in unpredictable conditions.

They left Washington, D.C. on July 7th and arrived in San Francisco on September 6th (five days later than planned). Their overall pace averaged about 6-8 miles per hour, and of course, by modern standards we'd consider that abysmal. For reference, the modern journey (via Google Maps) is a 42-hour drive; assuming you travel 8 hours a day and occasionally hit some traffic or wait for an accident to clear, you'd arrive a little less than a week later. Not so in 1919! You can read a daily log of the trip here, which is fascinating. It's a litany of broken vehicles, busted tires, constant oil changes, and complaints about poor road conditions. While Eisenhower's support for the Federal Highway Act of 1956 is usually credited to his observations on the German autobahn during WWII, the misery of that long trip to San Francisco played an equally important role for him.

This is a very accessible Slate article about the trip if you want a quick look.