I definitely wouldn't go all the way to Japan for 7-10 days. With a 12 hour plus flight and jetlag to contend with it definitely wouldn't be worth it IMO, especially when there is so much to see and you really need to travel around.
I'd go to Morocco, do a tour out to the Merzouga desert via Ait Benhaddou, mud kasbahs etc. If things weren't blowing up in the ME then I'd recommend Jordan, Petra and Wadi Rum are mind blowing but there are lots of other sites too and the country is small enough to be very easy to get around.
Or the Caribbean - Grenada and hang out on Grand Anse/Mourne Rouge beaches and do a few trips to see chocolate being made/George town/Grand Etang NP etc (a longer flight but a more chilled holiday suited to a shorter time). Or the Cayman Islands to swim with giant stingrays.
In Europe I'd go to the Dolomites. Just about anywhere in Italy really, or Croatia. I haven't been to Madeira and the hiking looks awesome, or Slovenia - some very beautiful looking areas there.
I've travelled a lot on my own, best thing IMO is to just plan carefully, book it all - and so give yourself no choice but to do the scary (but amazing) thing.