I'd be inclined not to utterly upend the existing city spread system (as is, the territorial size of cities relative to the entire world is exaggerated to integrate urban combat and city planning into the world view) but I would be interested in, say, making Railroads be the technology which allows for Industrial and Entertainment buildings to spread their influence out to 6 tiles. (Maybe prior to them, they only radiate out three tiles.
The increasing Spread Influence is an elegant solution: stays within that current game mechanics and provides a substantial bonus to the Civ involved. Historically, of course, the Influence would spread to virtually all cities connected to the Rail network, but that's probably Way Over The Top. I do think the actual distance spread should not be fixed, but dependent on Map Size to make it proportionally as influential.
Certainly I think Railroads should be a key technology dependent upon Steel and the Economics tech route.
Sounds to me like requiring a load of production or gold to obtain the railroad building unit would simulate the production and economic expense, perhaps with a "Railroad Tycoons" economic policy to reduce their cost, later becoming a "Transport Infrastructure" policy in the Information Age.
If the Railway building unit acts like a Trader, maybe they have a high maintenance cost while active (simulating the massive expense of building long lines) and if it acts more like a Military Engineer perhaps it could incur a gold cost when you use it.
The source of the Gold required could be a Civic: Rampant Capitalism, which dramatically increases the Gold per Turn in the Civ, (perhaps based on the number of Banks in the Civ) while, every 6 - 10 turns the amount of Gold would be reduced by 50% for 1- 3 turns to represent the periodic Panics, Recessions, or Depressions caused by unscrupulous Speculation. This Civic might be replaced/negated by Central Reserve Bank Civic in the (late) Modern Era, which stabilizes the amount of Gold per turn.
This way, the Railroad would require both Tech and Civics, which would also reflect the massive changes required in finance and industry to build them.
I was all ready to require more 'railroad upgrades' in the Information/Atomic Eras, until I did some research on the US Dept of Transportation statistics, and discovered that by pure Tonnage Carried, trucks outweigh railroads by almost an Order of Magnitude in the US of A now. The reason is the Interstate Highway System and the greater flexibility of truck traffic, which has virtually taken over all the mid-range and short distance freight transport. I'd still like to see the railroads kept, but if we were being really accurate (not that Civ games ever were!) in the Information Era the railroad graphic would be replaced by a multi-lane highway with trucks moving along it and a faint soundtrack of diesel horns and country & western music...
I think a railroad station district is the best option. Have it connect automatically to other railroad districts and make it so units can immediately move from one station to the next 2-3 in one turn. I prefer a separate district and mechanic than lumping them in with roads, they should be separate.
The problem with having a separate District is three-fold: on the one hand, many of the major passenger terminals are Central of Union stations in the city center. On the other hand, many of the effects of the railroad are connected with Commuter Traffic by rail into the city center, which allowed suburbs (Districts) to spread out since the Industrial Era. Finally, the great Industrial/Production increases brought by rail were due to the railroad delivering right from Factory to Factory - that is, from Industrial District to Industrial District.
One possible solution, because the separate District does keep the railroad in line with current game systems, would be to have a Railroad District that, for full effect, must be placed adjacent to the City Center AND the Industrial District. This might require, as it frequently did historically, the 'tearing up' of an older District to make room for the railroad, but it would neatly cover all the Requirements.
The Buildings possible in the Rail District would be:
Passenger Terminal - Industrial Era. - Or a possible Wonder of Grand Central Station/Victoria Station, or such - Population Growth increase from Immigration from the countryside, allows Influence from Entertainment Districts up to X+ tiles away (twice or more previous Influence Distance)
Freight Marshaling Yard - Industrial Era - Production increase to all buildings in the Industrial District or Ruhr Wonder, Influence from other Industrial Districts up to X+ tiles away as from the Passenger Terminal for Entertainment.
Container Yard - an Atomic Era Building, representing the vast increase in trade/transport caused by 'containerization' starting in the late 1950s. This would increase both Gold and Production in the city, AND increase Gold from any Trade Routes to/from the city.