A few years ago we had a 3 week holiday in the western US. We shipped our bikes over, did 5K miles in 3 weeks, through 6 states and saw loads and had a great time. I don’t think that itinerary would be fun in Europe but the US is empty with very little traffic compared to Europe so 4 months should be ample.
I mention this because of the old adage ’the slower you travel, the cheaper it is’.

I don’t like giving advice because everyone is different but this is what we do on our yearly 4/5 week holidays in Europe.

We camp, although if the weather is horrendous we’ll rent a cabin or caravan for the night - unfortunately the rise of ‘glamping’ has made this option very expensive in Western Europe so a room in a house is often a lot cheaper.
One of the main advantages of camping is that you can buy and cook your own food which saves you a lot of money. So, even if we’re somewhere that a room is the same price as a pitch (eg Balkans) we’ll pitch.

A typical trip looks like this:
We will travel on small roads (motorways/autobahns eat up petrol). We stop and buy sandwich ingredients (not ready made) and fruit around midday then stop at the next attractive place for a picnic. There will be stuff left over, cheese etc for tomorrow. We drink water from our camel backs - I believe these are a must.

We usually stop around 3pm for a coffee - usually in a cafe but occasionally brew our own if we are somewhere remote.
We will start looking for a campsite around 5pm - they’re plentiful in Europe. We prefer council or farm sites, rustic and cheap.
After pitching we will wander into the nearest town and buy ingredients for dinner and a cheap bottle of local wine. We will also have one in a bar.
In the morning we will have porridge and coffee, which we carry with us, then strike camp.

We travel like this for around 3 days, stopping at places that we want to visit then we’ll settle somewhere for 2/3 days - obviously somewhere that warrants a stop. We can greatly reduce our spending when we stop: at least 1 day no petrol, then we’ll use 1 bike for visiting/ local trips. At least 1 day just lying in hammocks.
Then we move on.
For us, things that use up most money with little return is eating and drinking in restaurants and bars. Lunch is cheaper than dinner in restaurants so we very rarely have an evening meal in a restaurant - special place or occasion only. Lunch can be a good, large cheap meal in some countries so we might stop for one occasionally then we just need a snack in the evening.

I think the US and Canada are comparable to Europe so take from this what you will.
We are hoping to ship into the Eastern Seaboard in September and head south.
Enjoy your trip