Mera Peak is said to be possible without any climbing experience, and it looks like the trek from Lukla is about 2 weeks. Is that true? How hard is the trek -- Looks like it requires well above average fitness level?
If you are significantly overweight or have dodgy knees, then it isn't for you. You are moderately fit and prepared to do some long walks in preparation, then you are probably fine. If you aren't sure, maybe go on one of the lower level treks and see how you get on.
Aconcagua in Argentina. It's on my 'things to do if in the area' list. The nearest airport is only a 200km drive on a tarmac road away and then a 40km trek to the peak! Although the 4km altitude gain is likely to be harder than the distance.
BTW Everest is so steep that it doesn't have a lot of snow on it compared to other high mountains. So it is not even a very attractive mountain (subjective obviously).
That altitude was about my limit even at the time. I had done a couple of previous Nepal treks to fairly high altitude but not actual climbs and had done a lower altitude glacier climbing school in the US northwest.