Local will depend on where you are. Use your common sense 
For example, an Isle of Man landline might be +44 (0)1624 812345. The +44 identifies it as UK/Isle of Man, 01624 identifies it as Isle of Man landline, and the 8 identifies it as a landline in the Isle of Man (kind of confusing but trust me on that). So the answer for someone with that number would be 1.
I want to see if there’s an interesting distribution.
In a north american phone number I want the 2 from 111-111-2111.
I’m not sure I get it. My number is (000) 123-4567. What should I answer?
4, I think.
In the US, a phone number would be like 987 654-3210, where 987 is the Area code, 654 is the exchange, and the last four don’t have a name AFAIK. Area Codes were, and mostly still are, non-overlapping, so those wouldn’t be what you want. The 654 prefix is local to an area, but isn’t the only one. A single area might have 654, 653, 652, 553, 552 all servicing it. There will be several/many prefixes covering an area. The last four are assigned randomly*.
So in this case, do you want “3” for this poll? That would be my guess, but I’m not sure.
This is for landlines, not cell phones.
I’d say 0. As far as I can tell, the area code is the only geographically linked component of our phone numbers (besides the country code).
It does note about the 123 section:
So it’s tied to a geographic location, but not yours, or one that’s near you, necessarily.
Looking at the other responses, I’m not sure. OP, what do you want from us?
I would like 4 in tdn’s situation, 3 in zenbeam’s situation
When I was growing up in a small town in New Mexico it was (505 NM area code) (three digit local geographic indicator) (four random digits)
Every body in town had the same three digital local geographic indicator. People in the next town had a different one.
Ah, OK. 7 it is, then. 
In that case I should have voted 4. It doesn’t have any “local” connotation to it. As far as I can tell, in my area nothing past the area code (first three digits) has anything to do with where you live. Some exchanges (second three digits) belong to the company issuing them (359 = Surewest) and the rest seem random to me. As far as the last four numbers go, I’m pretty sure they are completely random.
The telephone people use this when describing:
NPA-NXX-XXXX
NPA is the area code - these can overlap - but back in the day were unique (80s at least) and ALWAYS had a 1 or 0 in the middle. You could tell big cities as they always had short numbers (think pulse dialing - took less time at less wear and tear on switches. NYC is 212 - the shortest possible - while somewhere in Alaska is doing to use 8 or 9s.
NXX - these used to be unique as well - and NEVER would have a zero or 1 as a first or second digit. Same now with first, but not second. These used to be assigned to each CO. There still is a fairly decent geographic component to these.
XXXX - other than when a phone company reserves numbers - these were usually somewhat random - although many times the phone company would reserve 99XX for internal testing and 97XX - 98XX for payphones.
Anyway - you aren’t going to find ANYONE in the us with the NPA first digit as a 0 or 1. And it will be biased to 0 and 1 for the second digit based on the old numbering scheme.
And for the NXX part it would be the reverse - second digit - almost everyone is not going to have a 0 or 1 as the second digit of the NXX (but some will).
For the XXXX part - AFAIK - randomish.
Ok, this is one of two polls that don’t make sense.
I have no idea which digit you want for a US phone number.
And my phone number only has one last digit to it, it doesn’t have a second last digit.
I’m sorry. My phone numbering doesn’t fit into your poll.
The phone numbers in Canada are in the standard ten-digit North American format of +1 NPA NXX XXXX, where NPA is a three-digit area code.
Previously, the area code was optional, not to be dialled on local calls. However, most of the area codes in Canada are now in “overlay” areas, where more than one area code is active in the same area. As a result, we have to dial all ten digits of the phone number, including the area code, even on local calls.
Area codes where I am sitting right now, in the extended suburbs of Toronto, can be 289 or 905. Just over the hill, a five-minute drive away, is another area with codes 705 and 249. Many numbers in all four of these area codes are local to me. Thus, local numbers I dial can start with 2, 7, or 9.
Then there’s Toronto itself, 60 km away. It has two area codes, 416 and 647. People there can also call some 289 or 905 numbers locally. So they can call numbers starting with 2, 4, 6, or 9.
And they’re adding two more area codes to the region in 2013: 365 for the 'burbs and 437 for the city of Toronto. So then people will be able to dial numbers starting with 2, 3, 4, 6, or 9 locally from Toronto, and I’ll be able to call numbers starting with 2, 3, 7, or 9 (assuming I’m still here and haven’t died or moved to Hawaii or something).
And I’ll add that though I sit in the suburbs, I’m using a cellphone with a Toronto number in area code 647. I dial out as if I were a user with a local number in area code 905/289, but people calling me have to call 647.
So for purposes of the poll, I’ll put down “6”.
In a north american phone number I want the 2 from 111-111-2111.
I’ve certainly learned something about north american phone numbers at least here! I pretty much knew how the formatting system worked; what I didn’t realise is how my question would be completely misinterpreted due to the empahasis on local
I’m not sure how Australian phone numbers fit into the OP’s schema. Here in Newcastle, phone numbers are +61-2-49XX-YYYY (or 02-49XX-YYYY from inside Australia). Before there was some reorganisation of the phone numbers in Australia, to add room for expansion, they used to be 049-XX-YYYY – those were the days when people rarely directly dialled international calls. The XX represents an exchange, and the YYYY was assigned to phones linked to that exchange. So I suppose the first digit of the YYYY group is what the OP is after.
But in the local area, any local area in the NANP, that digit could be any digit from 0 to 9! It is in no way an indication of whether a number belongs to a particular locality; that is indicated by the combination of area code and exchange code.
For instance, consider the village of Sutton, Ontario. It is located in area code 905 and 289. It has local exchange codes 905-596, 905-722, and 289-576. Link. Any of these exchange codes can have “line numbers” from 0000 to 9999. But it’s the exchange code and area code that are tied to the “rate centre”, which determines the location the number is deemed to have.
Now, if you’d just said, “what’s the first digit of your line number”, and left “local” out of it, I would have said “0”. 
Is this part of some bizarre Nigerian scam to get our phone numbers?
It’s actually a secret Manx plan to assemble a ‘composite’ North American phone number that will, like a skeleton key, be able to tap into every phone acc–oops. I’ve said too much.