Hey anonymous Scandinavian neighbor.
I have myself been in your shoes, and never seemed to get a proper answer, simply because the US mobile market seems totally screwed compared to the "Scandinavian" offers.
I travel to US often too, and have ended up in using T-Mobile starting with a $30 Walmart Starter pack. It had unlimited talk, text and "unlimited" data with 5GB on 4G (EDGE after 5GB).
I wanted to keep the number, so when home I change the plan to "Pay as you go" (no roaming available) which is a $3 monthly plan, this is just to keep the phone number. If you don't need it you can discard it.
When I return to US I simply change the plan to whatever suits me (usually $80 everything unlimited plan).
I usually travel west coast, but coverage has been fine, though some holes in desert/rural areas. And yeah even on 4G there can be areas where speed is slow as EDGE probably due to overloaded cells.
If you go for this idea, there are some things to remember.
- If you want to keep the number you have to register an account with My-Tmobile while in US due to SMS activation (since international roaming is an extra service/fee)
- When changing plans there is a turn period. Usually I change the plan near my departure and make a chat session with customer service and ask them to make the change of plan immediately, rather than have to wait. Funny enough, downgrading a plan is effective immediately.
Of course this might not be the best or cheapest option, but it was the easiest and has been for me.
The Google Fi project has been looking promising, but the requirement of a Nexus phone does not please me.