US citizens can stay in the UK for six months as “general visitors” so it would be easy to use it for that. There is no hard limit on the number of visits or total duration of stay (but see the note at the end).
Croatia already applies rules very similar to the Schengen area and should eventually join it (as do Bulgaria and Romania). For the time being, it should however be possible to go there and come back to the Schengen area repeatedly if you stay for some time in two of these countries (otherwise there would be one day missing, by my count).
Turkey, Ukraine, Serbia all have a limit of 90 days in any 180 days period so you could go there too, with the same caveat. In Turkey, US citizens do however need an “e-visa”. It's mostly a formality, not too different from an ESTA, but it means you have to pay a fee.
In any case, border guards in the Schengen area and elsewhere should in principle check a number of other things (purpose of the trip, financial means, insurance, etc.) even for people who don't need a visa. If there is something suspicious, a border guard can always rule that they don't believe the stated purpose of your visit and send you away, even if you have never overstayed.
They are not always very thorough but if your stamps reveal several long stays, they might be more careful so you need to make sure you have everything in order. If you are genuinely visiting various part of the Schengen area and you can show you are sufficiently wealthy, you should be OK but if it looks like you have been working illegally in the Schengen area or are always coming back to the same place, you could be denied entry.
Same thing for the UK, where this is actually the main way to prevent “hidden” residence since they don't have any hard limit on the duration of stay beyond the six months per visit rule.