Planning a 3-week Tour to the US
 

I am planning, together with my father, a 3-week tour to the US anytime this year. If it's in June, I will have to attend a conference for 3 days in Chicago. We will also need to visit a friend in Rhode Island. The budget is about $4,000 per person/all inclusive. My questions are: When is the best time to visit all major states? Is it best to do a road-trip or fly from a state to another? How much luggage to carry? Where to stay (lodges or hotels)? Las Vegas, California, New York, and Grand Canyon must be included. I like undiscovered small towns, countrysides, desert areas, cities with local vibes, etc. I know this is quite vague, but I'm open to suggestions. Many thanks.

Three weeks is not nearly long enough to visit the places in your post nor a fraction of the states you tagged.

What you described you need at least a year... or more! I don't think it is realistic to think you can visit 50 states in one trip regardless. Although I'm not sure what you mean by "major states"? Seriously to do everything you mention would take a lifetime.

You don't have enough time. You could fly from Chicago to LA or San Francisco and do a coastal drive plus Yosemite and maybe Sequoia national parks but you would need advance reservations for the parks. $4000 divided by 21 days is about $190USD per day per person. A decent LA area hotel would run about $200-250 plus 15% room tax.

Where are you coming from? If you are coming from somewhere to the west (Asia, Australia?) fly to Chicago first. If you are coming from the east (Europe, Middle east etc.) fly to Boston and go to see your friend in Rhode Island first. If you would prefer not to fly within the US, you can use trains between Boston, Providence Rhode Island, New York City, Chicago, Denver, San Francisco and Los Angeles. It takes about 3-3.5 days to go from one coast to the other on trains.
It took me about 14 years to visit all 50 states.

Oh I missed the budget part. Yes that also is not realistic or feasible. $190 per person to include transportation between states by flights or rental car, a place to sleep, food, admissions, etc.

Since you want to go to Chicago - Rhode Island - Las Vegas - California - New York - Grand Canyon all as "must be included", you need both more time and more money.

Best time to visit is probably Sept/Oct when weather is still good everywhere but your budget will go a lot further than in July/ August....especially in coastal California or the east coast.

With 3 weeks you will just be doing a lot of driving and looking out the window. Or looking out of train windows. I would decide on maybe 5 or 6 cities/ states to concentrate on. Max. If you chose 6 destinations, then 6 of your 21 days will be spend either flying or driving between locations. And your arrival day into the U.S. and your departure date from the U.S also don't count as sightseeing days. So you'll ended up spending only a day and a half visiting/enjoying each place and its surrounding towns.

Focus on Chicago, then head east to your friend in Rhode Island. You can see Boston, NYC and Washington DC. There is plenty to keep you busy and happy for three weeks with these points. Leave states to the west for another trip, simply not doable in driving and very expensive in flying, especially in summer months.

If this is a drive through trip with little time in any one place, just been there, kind of trip you could do the following

Day 1,2,3,4fly to Boston, look around, train to RI,visit friend
Day 5,6,7,8 train to New York check out city
Day 9,10, 11,12,13 fly to Las Vegas, rent a car drive to Grand Canyon, visit other sites in the area
Day 14,15,16,17 fly to San Francisco, or Los Angeles visit that area
Day 18,19,20,21 fly to Chicago then home

The lodging will eat up more than half of your budget unless your friend in R I hosts you for those night and your business in Chicago is covered. You would have to research flights, but can often get low fares between the cities.

The trip could be done in the reverse, but that would put you in peak tourist time when lodging and air fares tend to be more expensive.

Unless the OP returns we are just throwing things against the wall to see what sticks (he tagged it for eleven states and includes at least two others in the post so sort of hard to take seriously)

Lets hope the OP returns. Any nights spent on Amtrak trains are nights not spent in expensive hotels. The Lake Shore Limited travels overnight from NYP to Chicago. The Chicago HI Hostel (largest in the US) is about the cheapest place to stay in Chicago. The upper floors are used as dorms for a couple colleges.