I'm meeting with a local incubator tomorrow and I would like to know if it's okay to tell them I'm going to "shop around".
I want to talk to other incubators and see what they can bring to the table.
Is that okay? Or do I risk missing out on their offer?
It's better not to say that; it can come across as a lack of enthusiasm for their program or an arrogance-tinged expectation that they should be competing for you (and these programs almost always have more qualified applicants than they can admit).
Anyone applying for any incubator should research and consider several. It's fine to ask questions about how they compare to a different program. But ask about specific details, like: "I know Incubator B invests directly for equity, whereas you provide a convertible note; can you talk about why you choose to do it that way?" -- if you ask a broader question ("How are you different from Incubator B") you're likely to get a non-answer about not knowing all the details of how Incubator B works and then reiterating some of their incubator's usual pitch.
You don't mention what stage this meeting is. If this is like Y Combinator's in-person interview where a final decision is made, this is way too late in the game to be shopping around. By all means research alternatives on your own, but if you send signals of hesitancy, don't expect them to consider you further.
I'm going to come at this from a UK perspective and widen slightly on investment in general and not just incubators.
I'm also going to perhaps speak from the "ideal" point of view, which i appreciate for cash-strapped start-ups isn't always the reality.
But getting investment is like a marriage. It's about two parties seeing if they both want to work together. You need to be confident that they're also right for you.
VCs will often ask who else you're talking to. And in my view you'd be mad when asked to say no-one else as this suggests:
1 you're lying; or
2 if no one else is talking to you, have they over-estimated your product; or
3 a lack of drive and commercial acumen. If you're only talking to one VC you really aren't making enough effort.
Appreciate incubators may be different, but all the same, think this stacks up in wider investment discussions.
Hope all goes well for you!
When you arrive, say "I'm just here to learn more about your incubator"