There are plenty of places like that, but you have to consider that remoteness is relative to other places. Even in a major capital you will find small neighbourhoods that are a pain to get to, even if getting there is not particularly difficult - like a district with poor public transport that you need a taxi to get to. Note, that they wouldn't be completely isolated, but would require more effort to get to than similar settlements.
Where would that be?
* Islands are a pain to get to, because you need either an aircraft which is expensive or a boat which is slow. See Pitcairn Islands, Svalbard, Galapagos, for less remote - Channel Islands. The limited space available also tends to turn the whole islands into one large settlement.
* Mountainous area can make transportation difficult and dangerous, especially if the town is surrounded by passes. These do not have to be fa away from other settlements, but the trouble to travel might add to the remoteness. Also, mountains hinder aerial traffic, as bad weather or low visibility interferes with navigation.
* Great wilderness is another example. Siberia features quite large cities being so remote from Moscow's point of view, that they are grouped around each other, with little access to the most populous regions. You will find that in such environment building a large city is preferable to several smaller ones, due to cherry-picking favourable locations and strength in numbers. See Siberia (Magadan) and Canada.
* Desert is a similar environment. While large oases with artesian wells can support large cities of thousands of people, small settlements would be scarce to the point of negligibility.
* Marshes and wetlands - some cities can be considered remote for only certain parts of the year. During monsoon season in Asia or wet season in Africa many settlements become isolated, because suddenly there are rivers everywhere, terrain is flooded and it rains all the time. Some people have to literally arrange their life around their village being cut off from civilisation for half a year.
But why would anyone live there?
That is you main concern. 87
There has to be a strong incentive for people to build and support large cities in the middle of nowhere. Examples follow:
* Wealth of natural resources - especially if it's scarce or very valuable, like rare earths, oil, uranium, precious gems but also valuable flora and fauna for hunting, lumber etc.
* Important trade routes - desert cities might be in a middle of nowhere with little resources around, but supplying caravans with food, water and shelter enabling trade is one of the foremost purposes for existence of such cities. You would find such cities are extremely wealthy but with costs of living to follow.
* Strong military positions - you must not forget that sometimes forts are placed in mountain passes or islands with little to offer, just for the sake of being a highly defensible area - a gateway to your state or conversely a stepping stone in case you would like to invade your neighbour. Soldier's families, providers of entertainment and all that follows form a city nearby.
* Religious settlements - monasteries and cloisters are often placed in remote areas seeking isolation as a philosophical or religious ideal. Surely, supplier satellite settlements follow to trade with the good monks.
* Artificial cities - China is the leader of building cities in the middle of nowhere for the sake of central planning. Soviet Union did similar. The process implies that some central authority looks at a map, sees a blank space and thinks "well, if we had a city there everyone would benefit...". This is also how you get 10-lane carriageways from nowhere to god-knows-what.
How long is too long to travel?
Nowadays you can get almost anywhere if you have a plane or a helicopter. This is basically your "travel anywhere" perk. However, travel by planes is restricted by airstrips (though a city would have one if it's needed for sure), bad weather (constant fog, high winds, frequent storms) and terrain (mountain peaks, having to land on a slope).
With that in place you might find that roads take days to travel by 4x4 car, especially in the winter and railways are too expensive to maintain or impossible to build. Remember that dangers of the travel might be more important than length. If every year several trucks are being buried in mud or lost in an avalanche there might be little incentive to use that mean of transportation.
Travel by sea can be equally perilous. For the longest time Galapagos Islands remained unexplored because access required sailing around Cape Horn, a feat of seamanship that not every naval vessel could boast. With advancements in sea travel most places are definitely reliably reachable, but it might be simply too expensive and uneconomical to maintain frequent sea routes. 207