Wow. A couple of months seems like a long time, but when you're talking North America, you could take a couple of years and not see very much at all. It's just so huge here compared to Europe. We think nothing of driving 4 hours to visit friends and family. I have family that lives 5 hours away and I just hop in the truck, go visit and come back the next day.
Trains in N.A. are wonderful for meeting people as long as you have NO SCHEDULE. Honestly, it should be 4 days from coast to coast, but just 2/3 of the way across set me back 4 days. We were so late, they were running out of food on the train. If you do go train, get a berth. Economy is just a seat and very uncomfortable for more than 8 hours. First class with a room sounds good, but the rooms are like little jail cells. An upper berth is great. You get a nice comfy, roomy seat for the day and you can visit easily. At night you have a little hobbit hole to curl up in. Unfortunately the timing of a cross-Canada train trip sucks because you miss a lot of the scenery while you sleep.
But, using the train from one place to another would work well.
I would start in the south in April (that is southern US states) and then move north. April can still be chilly and rainy in many parts. Frosts are not uncommon in April in most of the northern states and Canada.
No one has said much about Canada yet. Probably because we are all too stunned to be able to say what NOT to see. See EVERYTHING, but how in only 60 days? I will mention only Canadian things.
Big cities in Canada to see: Vancouver (bicyle), Toronto (city transit), Ottawa (bicycle), Montreal (city transit), Quebec City (not sure how to get around there). Way to much to see in each of these: architecture, zoos, museums, ethnic neighbourhoods (see the world in just one city
) A million smaller cities that each have their own uniqueness.
Rocky Mountains in British Columbia, Yukon, Alberta and Appalachian Mountains in Quebec, New Brunswick -- but these are much smaller than the Rockies, so if you have to miss one set, do the Rockies. There are day or overnight horse trail rides through the Rockies. My sister did one and it was amazing.
The Prairies in Alberta, Saskatchewan and Manitoba. Miles and miles of green in the spring. It goes on forever. Great horse country in Alberta.
The Great Lakes -- these are amazing. You absolutely will not be able fathom the size of these. You MUST take a boat tour of at least one of the lakes. In Ontario, the 1000 Islands cruise is nice; there is also a ferry across Lake Huron I believe -- Cheechiman ferry to Manitoulin Island. Niagara Falls is big and pretty but very expensive and once you've seen the Falls and the Casinos, well, there isn't anything else in the spring to see as the vineyards won't be in season. The Great Lakes border the US and Canada so go from either side.
Tundra -- very north. You'd have to be a true outdoor enthusiast to have this make sense for you to go. Northern Alberta, Yukon, Northwest Territories, Nunavut and Northern Ontario. Probably very expensive and only worth doing if it's your bag. Definitely fly-in locations only.
Lakes, rivers and more water -- Ontario has an unfathomable number of waterways. If you enjoy water at all, consider day trips on water. Whitewater rafting, fishing, canoeing, kayaking, -- if you want to do beaches, do those in the southern States. Canada has some beautiful beaches but very cold until late May / June. Sandbanks Provincial Park in southern Ontario would be about your best bet that time of year. Eastern provinces have beautiful shorelines. Newfoundland / Labrador is the extreme of water, land and culture, but very out of the way. I've heard there is nothing like it anywhere, but never been there.
P.E.I. bridge -- one of the longest bridges in the world. It was deliberately built with curves so drivers wouldn't get bored.
Take a ferry -- in British Columbia, Ontario, Quebec, New Brunswick
Culture -- Ontario, Quebec, New Brunswick -- check out the logging and forestry tourist attractions. This country was built from our trees. Sugar bushes will be done by the time you get here unfortunately. They run in March. First Nations culture -- I don't know about the rest of the country, but in Ontario there is a pile of stuff from the Indians to see.
I have to stop now. I'm getting myself confused trying to think of things and I haven't even begun to list activities / adventure tours. Time for someone else to continue on.
Forgive any typos. I haven't proofread this.