What are some tips for a U.S. citizen visiting Japan for the first time?
A number of things.
Keep some aspirin and eye drops on during the long flight - you'll need them.
Try to keep a light schedule the first day, and watch out for jet lag.
Study the history of Japan and the places you are going to visit ahead of time - it makes your trip so much more meaningful.
Do your research. Nothing is worse than wasting time - plan your trip carefully. Know where you plan to go, how long it will take to get there, etc. Carry paper or digital maps of your destinations. Don't slap your head after your trip because you just found a place you wish you had visited. There are several comprehensive sites you can look through, such as Japan Guide or the JNTO. Many official city and town webpages have their own sightseeing info on them in English, Korean and Chinese, and often you'll find good places that are listed nowhere else.
Youtube can also be an excellent resource - many ex-pats and travelers put up videos of good places to see. Try browsing through:
Have a back up plan. Stuff happens - someplace is closed, the weather sucks, you suddenly find someplace better you'd rather see. Know the opening/closing times of places (some stop admittance 30 minutes before closing time), plus each morning check the weather forecast and plan accordingly.
Next, learn about Japanese manners to avoid looking like an idiot while there.
The truth is that few Japanese can speak English with ease. But that doesn't mean you are completely up the creek. If you get hopelessly lost, which is very easy in Japan, it is better to find some older school or college age students and write out your questions in simple words. Japanese are still very poor at speaking English but are often glad to help you out if you lose your way. Carrying a business card or paper with your hotel's address on it can be a big help.
DO NOT just simply buy the Japan Rail Pass. Make sure that getting a rail pass is worth it first, given your itinerary, and don't just think any rail pass is a guaranteed money saver. There have been a few persons giving this bad advice to just automatically get one, and may be costing some people a lot of money. It may be that a regional pass might save you more. And unless you travel enough, no rail pass might help you at all. Flying on a low cost carrier like Peach, Jet Star or Vanilla Air for very long distance trips might make more sense than the trains also. ANA's Experience Japan Fare or JAL's clone of it can save you a ton.
You can see regular fares, routes and schedules on Hyperdia.com - use it to plan your trip better. Japanese trains are extremely punctual.
Learn as much of the Japanese language as you can - whatever you learn will make your time in Japan better and more productive. For learning Japanese, you might look at Learn Japanese Free, 123Japanese, or JapanesePod101.
Know metric conversions - nearly the whole world is on the metric system, and you will have to use it to get by. Such basic things are 23kg (50 lbs) - the typical airline suitcase weight limit, 1 mile is approx 1.61 km, 2.2 lbs = 1kg, 2.54 cm = 1 inch, 500 ml = a bit over a pint, 20°C=68°F, 30°C=86°F, etc etc.
If you are in Japan during the summer, be ready to sweat your behind off. Carry enough deodorant with you and if you really hate humid weather, plan a trip up north to Hokkaido or the Tohoku region.
Take all the OTC meds you think you are going to need - eye drops, aspirin, vitamins, allergy pills, sunblock, antacids, deodorant, cold meds etc - prices for them in Japan are pretty much highway robbery. That said, do not take anything with psuedoephedrine or opiods, or you could land yourself in hot water.
Carry a thin calculator, calculator watch, or a smart phone with a similar app for understanding prices.Many cities have a tourist info office in their main station - use them. Often you can get free maps and helpful info.
Carry tissues or hand towels with you – most of the public bathrooms don't have hand-drying facilities, and a few don't even have toilet paper.
Unless you want something fancier, a business hotel is often a good place to stay at. They are not fancy, but they are quiet, clean, inexpensive, and often conveniently located close to the train station. Many throw in breakfast for free, and have free wi-fi in their rooms. Some are Super Hotel, Toyoko Inn, Comfort Inn, Route Inn, Dormy Inn, and the Japan Economy Hotel Group. In Tokyo, there are actually some places that are even cheaper. And if you will travel all over a city, look for some sort of train, subway or bus day pass. Kyoto has a bus pass for 500 yen. Tokyo has a 3 day subway pass for 1500 yen. And so on. JR Passes are often of little help in local transport, although within Tokyo you can go to many popular places on the Yamanote Line, in Osaka there is the Loop Line, and in Hiroshima there is a loop bus that takes the JR Pass.
There are many ways to save money, if you travel smart.
1. Carry the business card from your hotel with you. The address in Japanese can help if you get lost.
2. Domestic transport can get expensive. Costs can be rather high for relatively short distances.
3. Try a wide range of Japanese food, from street food (perfectly safe) to high end specialty restaurants. Most Japanese food in the USA is a pale imitation to the real thing.
4. Also take the time to visit small villages and rural areas. Japan is an incredibly beautiful country.
5. Used cameras are a good value. Many more models are released each year in Japan than abroad and it is easy to find cameras only 6 months old at huge discounts.
6. Stay at least one night at a ryokan (traditional inn). Yes, they are expensive, but usually include very good dinner and breakfast (along with having your first truly civilized bath). This helps offset the expense.
7. If you get lost, most Japanese people are extremely helpful, often sometimes accompanying you to make certain you get where you are going.
8. 7-11 has ATMs that accept foreign cards (as do Citinank, HSBC, and the post office).
9. 7-11, Lawson, and Family Mart have cheap food that is safe and tasty.
10. Try a bento box on the Shinkansen. Different stations are famous for different types of bento.