Which lens/lenses would you recommend for this particular occasion on different budgets topping $500.00 or a lot less that could potentially serve us the most?

I am not a photographer and even if I am not planning to do this for living, I would like to learn how to take the best photos possible given the circumstances. I just purchased a D5200 since it seemed like a good deal (complicated camera, I should have taken your advice and get the more user friendly, comparable for the price, Canon). It came with an atypical lens for this model (AF-S 18-70mm). Now, I am traveling soon to a set of different places: Buenos Aires (architecture), El Calafate (glaciers & mountains including a a full day excursion sailing on a boat (glare etc), Iguazu Falls (Tropical waterfalls) and last but not least, we are going to Rio de Janeiro (Cristo Redentor, Pao de Acucar & Copacabana beach) Obviously, a real photographer would need more lenses in order to take the best advantage of the scenery. In my case, I am not a rich person and I am only looking for one or two lenses that are going to provide me with the most versatility on a budget.