I'm in NY. It's been suggested I limit the scope of my VC courting to my native coast. I appreciate the intimacy of the entrepreneur/VC relationship, but if I'm looking for early-stage funding, shouldn't I also cast into Silicon Valley? Shouldn't I try an identify the best-fit VCs regardless of where they are? (Yes, of course I have to pitch them at their location, but beyond this, how often will we really need to see each other face-to-face?)
But, it's not an absolute requirement by any means.
Your VCs are going to be involved in the company. Having them in the same time zone, and within driving distance makes many of the startup board meeting and advisory logistics much easier. Because of this many VCs are also reluctant to invest out of their own time zone, unless the idea is hugely compelling. So, you might end up wasting a lot of time and money courting opposite-coast investors if there is not a huge benefit to them and you.
I would advice you stick to local VCs for your early rounds, and explore more distant VC options when the value and path of the company is a little more defined.
While it's always ideal to have your VC as close as possible, it's fine to take some investors from the West Coast (or other areas) so long as you have routine contact with them and make an extra effort to keep them involved. Assuming you're doing a round with multiple investors, it's good to find one of them who is also NYC based so you do have someone who is more accessible and who you have more routine contact with (if this person is the lead investor for your round, all the better).
Every VC has their own philosophy for where they invest.
Often (but not always), the VCs outside Silicon Valley are far more open to investing in companies outside their area. Some of them (like Union Square Ventures) will invest anywhere if it's the right company.
Often (but not always), VCs in Silicon Valley like to limit themselves to Silicon Valley, although they may have some other cities that they are happy to visit regularly. For example, I've noticed that Kleiner Perkins' sFund makes a habit out of being in New York City regularly and they have a whole roster of companies over here.
As a matter of general principle, the average VC would invest in a company in downtown Tripoli, Libya if they thought it would make them a lot of money... no matter what they tell you.
In your situation, there are a lot of VCs in New York and a lot of Californian VCs are happy to invest in New York, so it's worth talking to VCs on both coasts.
We're Chicago based, and have taken most of our money out here, but then also took a couple of investments from the Bay area. It obviously depends on what you're doing, but for us it's nice to have that connection out there so we feel more at home when we go out there for business development trips. It makes our trips multi-purpose, and we're going there anyway, so it's nice to knock out a few birds with one stone. Plus it makes us feel really cool.