Ok, so... I don't know.
I mean, I live here so I don't know what I'd want to do here if I was a tourist on a short visit!
I guess it depends on what sort of trip you're interested in - vibrant, lively cities, majestic scenery in scarcely populated mountains and glens, historical stuff, modern art / culture, or a mix of a little bit of everything?
I used to live in Glasgow, which is an amazing city with a vibrant culture and a rich heritage. It's also the city of violent crime (it's fairly small, and there is more violent crime than in the whole tri-State area most years) but (and this is a big but) civilians are rarely the target. If you aren't bothering anyone, being a bit wide or joining a gang, you'll be fine. It's fine to wear jewellery there (I have a fair amount and I wear it most days). No one will bother you for it. As with any city, if you feel uncomfortable in an area, leave. It's ok, generally, if you don't go looking for trouble. "What are you looking at, pal?" is not a friendly question and should always be interpreted as the onset of hostitilies. If you hear it, run.
Edinburgh is the capital city, where the Parliament sits. Much more refined (and therefore not as much fun). Well worth spending some time there though, there's a lot to do. Museums (including the Museum of Scotland in in Edinburgh, and the National Portrait Gallery). Awesome restaurants and wonderful architecture. Royal stuff, if that floats your boat. Not as cool as Glasgow (and there is plenty healthy rivalry between the two cities) but still a very cool place to visit.
If you like nature and scenery and stuff, we have a whole bunch of that too. The Scottish Borders, the Solway Firth area and so on are at the southern end of the country, while up North you get mountains, glens, lochs and (depending on the time of year) an awful lot of midges and tourists. Midges will bite you, but the tourists are usually friendly. You can pan for gold in the Lead Hills if you feel like it. Or go fishing on Speyside. Golf at St Andrews is always popular, but if that interests you, book a loooooong time in advance and be prepared to take on the national debt of a small nation to play a round. It's eyewateringly expensive there.
There are whisky distilleries to visit, with wares for you to taste. Plenty of pretty places to eat wonderful food and lovely places to stay. Our beaches are incredible, but don't rely on it being warm enough to want to sit on them (ever). Wonderful for walking on, though.
The central belt is a good base for a shorter visit, and it stretches more or less from Glasgow to Edinburgh. There are excellent transport links there, and to the major cities. When you go more rural, using public transport will take a bit more planning (but of course can be done). Glasgow and Edinburgh are roughly an hour apart, less by high speed rail.
If you let me know where you're thinking of staying / what type of things you're interested in, I can make some suggestions. You're going to love it here, you really are!