If you are public transport your Ops Manual will tell you the answer, probably in Part A under "Determination of Aerodrome Operating Minima" or equivalent section. If you are private, you should form your own policy.
In our case, to select as an alternate, we need the forecasts and actuals to indicate that for +/- 1 hour from expected arrival the weather will be at or above the minima for the second best approach. I've paraphrased that last bit 'cos there's a whole table of choices, but broadly if the alternate has got an ILS and a VOR non-precision approach, you have to plan for the non-precision minima, if it's got a straight-in or a circling, you have to plan for the circle, etc. In other words, you have to allow for being unlucky when you divert. Of course, when you get to your diversion field, you don't have to fly the NDB-circle-to-land just out of spite even though the ILS is working
So, to go back to your question, the alternate depends on actual likely weather, not on distance. Where the topography is simple, a widespread forecast mist or fog can force an alternate 100 miles or more from your original destination. Where the topography encourages local weather variations, your alternate might be just over a ridge line (or whatever) where the weather is quite different. Although I have also heard the comment about alternates being "50 miles away" there's nothing magic about the distance - it's only the weather that matters, and there is certainly no requirement in our ops manual on distance.
And yes, on a reasonable day, your alternate can be just a mile or two away (although I believe it should always be a different airport - your destination could be closed by an emergency, a power failure or a blocked runway, not weather).