I remembered a thread long ago from the old FFG forums—this is back before Kingsport Horror was released, I think. Someone wondered about the maximum number of locations that could be closed at once. Now that Arkham is essentially complete, we can answer this conclusively. I'm going to take a try at it, but please let me know if there are effects or encounters I've overlooked.
First, some restrictions: I'm only going to consider stuff that comes from the eight expansions, and from FAQ entries. Things like the Summer League and Arkham Nights specialty scenarios won't count.
Secondly, I'm only going to count effective closures—closures that aren't transient. By that I mean the following: the Mythos card Strange Lights on Campus closes the three Miskatonic neighborhood locations until the end of next turn. Technically, that means through the end of next Mythos phase. The next Mythos card, however, could be Temperence Fever Sweeps City, which closes Hibb's Roadhouse until the end of next turn. That means that technically, all four locations are closed at the same time, but it's literally the last thing that happens on the turn with nothing else interrupting, after which the Strange Lights effect wears off, and this period can't affect investigators in any way. So they don't count as being closed together.
In the base game of AH, the best you can do is six locations closed at once:
General Store, Curiositie Shoppe, and Magick Shoppe when terror level is 9.
Library, Administration, and Science Building from Strange Lights Mythos card.
That's three temporary closures, and three permanent. It's no wonder why AH comes with six closure tokens. FFG did a good job of covering all of their bases. As a side note, you'll notice that the base game also comes with 20 doom/elder sign tokens, even though you'll never use all 20: Azathoth has 14 spaces on his doom track and it takes 6 seals to win. So an active game will have at most 13 and 5 in use: the other two are not necessary.
Each of the three expansion boards has its own mechanics for closing its locations.
Kingsport Mists will temporarily close the three Kingsport Head locations.
Specific encounters at Harney Jones's Shack (DH) North Point Lighthouse (KH), and First National Grocery (IH) will close those locations permanently.
Blight cards can permanently close Ma's Boarding House and Harney Jones's Shack (but the latter can be done by an encounter).
If you want to consider Shudde M'ell rubble tokens to be closures, there's seven more that can be included, with some redundancy.
Taking all of this stuff into consideration, here is how you can close the maximum number of locations at once:
Use all three expansion boards. Use Shudde M'ell as your AO, and The King in Yellow as your herald. You need the DH, KH, and IH expansions—or at least their Mythos cards—in play. The King in Yellow herald does not require KiY encounter or Mythos cards to function fully, so you only need to own that expansion to use the herald and the blights.
(+3) Get the terror level to 9 (permanently closes General Store, Curiositie Shoppe, and Magick Shoppe)
(+3) Have the three expansion encounters that close Harney Jones's Shack, North Point Lighthouse, and First National Grocery.
(+1) Obtain the Ma Mathison blight card, to close the Boarding House.
(+5) Gain the rubble tokens that destroy Newspaper, Bank of Arkham, South Church, Velma's Diner, and the River Docks. Two of these (Library, Admin) are redundant with Mythos effects below; and if you get all seven the game is over so that doesn't count anyway.
(+8) Fail the Nightmare Pool rumor*, drawing and resolve these three Mythos cards: Strange Lights on Campus (closes Science Building, Administration, and the Library), Kingsport Mists (closes Causeway, Wireless Station, and Strange High House), and Temperence Fever (closes Hibb's Roadhouse). Additionally, the Mythos card that was drawn the turn that you failed Nightmare Pool should be Fourth Of July Parade, which makes the Merchant District streets inaccessible in a way that is almost identical to closing them (almost: if an investigator is in that street during the onset of this Mythos effect, he must remain there. Normally when a space is closed, the investigator is booted out).
*Alternately, there is an encounter at Wizard's Hill where you can opt to force an additional Mythos card at the end of the turn for the cost of a very underwhelming reward (draw 3, spells keep 2). It's technically possible for this encounter to be gotten multiple times in a single turn. Strangely, the Nightmare Pool rumor opens a gate at Wizard's Hill. Funny, it's almost as if Wizard's Hill is a terrible, dangerous place.
Obviously, getting all of these conditions is not something you plan for, but technically the above is possible. Luckily for us, none of the effects are completely mutually exclusive. So far as I know, there aren't any effects missing from this list that are mutually exclusive with any of the listed items, either. There is a Harney Jones blight in the MH expansion that closes his shack, but the DH encounter will do: so MH is not required. Imagine that—Harney's death is preferable to his madness from seeing the King in Yellow play.
I want to make a note about the Mirage of Lakes KiY and Rails Are Washed Out environment cards. These disallow certain types of conventional investigator movement: the former limits your movement between two street spaces to following the black arrow, and the latter does not allow you to use train depots. Mirage was made only with the base game board in mind, where street spaces are cyclic. They were designed this way so that monsters always had a place to move to. However, the Dunwich and Innsmouth boards were designed to siphon monsters towards a vortex dead-end, so investigators following black arrows will be effectively disallowed from many neighborhoods, depending on where the investigators are when they move. This is not the same as space closure, since those neighborhood locations and spaces can still be reached by e.g. the Deputy Wagon or via an encounter or other transportation effect. Thus, these effects are not included in this analysis.
If you count rubble and Fourth of July as closures, that means the maximum number of spaces that can be closed at once is 20. Compare this to the 76 in-town spaces the investigators can visit (not counting Jail cells as separate spaces from their parent locations) - 26%.
If you don't want to count Fourth of July or streets, and are interested only in locations, then that's 19 locations out of a possible 55 (35%).
If you just want to know which spaces are permanently closed, then that's 13 (24%): if you get the 14th, that ends the game via earthquake.
If you play a game only with the Arkham board, then things get a little tricky. The Nightmare Pool rumor would not be in your Mythos deck, so you couldn't get those bonus three Mythos cards. The "best" you can do (that I can think of) is to use the "Ultimate Cosmic Evil" Difficulty Level card included in the Black Goat expansion to cause you to draw two Mythos cards per turn. Then we could have Terror Level 9, Ma Mathison Blight, five rubble tokens, and the Strange Lights and Temperence Fever Mythos cards drawn together, resulting in 13 locations closed out of a possible 26 Arkham locations (50%) or 35 Arkham spaces (37%). These are the highest values for percent of the visitable towns that are closed.