• Inflationary
• Hierarchical
• Scalable
• (Ideally, I'd love it if all of the "work" (computation) that is done to generate the currency actually did something useful)
• Might be nice if the 'work function' or whatever wasn't able to be run on GPU's, only CPU's.

(And of course, the features that we have in just about every cryptocurrency that's out there - decentralized, electronic, anonymous-ish, etc. I won't write about that stuff because we know it already)

A little bit about why each of these things -

Inflationary

Currency should be similar to nature. In nature, things that are 'old' get eaten up by things that are 'new'. "New bucks" should be worth more than 'old bucks'. Deflationary currencies like Bitcoin are the opposite; and encourage people to hold on to their money, effectively rewarding the "old" and punishing the new.

Secondly, there's a practical reason for this - "bad money drives out good" (Gresham's Law). People will spend the inflating currency, and hold on to the deflating one. That makes my new currency become one that is actively spent, all the time, and 'drives out' the "good" money (which would be Bitcoin, et al).

Hierarchical

Bitcoin and every other currency that I've seen all tends to be universal - if I buy a cup of coffee in Ocean Beach, San Diego, that transaction will show up in a ledger running in Adelaide, Australia. And it doesn't need to, it makes no sense to occupy the bandwidth. And it also means that there's a very strict chain-of-custody you can track for currency, and some privacy here might be nice. The rest of the internet works this way - when I grab an HTTP web page from a server in Mountain View, servers in the UK never see the request or response - because they're not involved, and don't need to be.

I believe Cryptocurrency should be the exact same. I'm imagining blockchains of blockchains, and them only talking to each other because a transaction passed across some hierarchical border. I'm imagining, maybe, a chain per continent, or something like that, and then maybe if it got popular enough, subchains per region, and maybe even sub-sub-chains. Of course, technically, I have no idea how we could manage to do that, but that'd definitely be one of the problems to try and figure out. I'm taking inspiration from a lot of the fundamentals of the Internet, here - routing protocols, layering, that kind of stuff.

Scalable

The whole "the block size needs to get bigger" thing sucks. Better to build in some of those lacks of constraint into the protocol. Maybe block-size is the trigger that creates a sub-blockchain, or something? E.g. if your "California" blockchain starts to get so busy that the entire blocks that contain transactions are starting to get full, that's when you spin up your "San Francisco," "Los Angeles, " and "San Diego" blockchains, maybe? Or maybe they somehow dynamically split off and form up some how?

But, regardless of the solution, the problem, simply stated, remains the same - "if something gets big you don't have to suddenly force everyone to upgrade their software."

Useful Work

It breaks my heart that all the Bitcoin mining that's done out there is all using pointless computations that serve no purpose other than wasting power. I would love it if it actually did something beneficial - like SETI at home, or some kind of cancer thing. I think I read about one of the newfangled currencies out there doing something like this. I would totally steal that concept.

CPU only?

This is really just because I like the egalitarian nature of this. I like the idea that the "little guys" can mine just as hard as the "big guys" and might somehow manage to get a payoff. Highly parallelizable work functions end up making people get custom ASIC's and GPU-rigs and I don't like that as much. But that's really just a "nice to have."

(edit)

Notes

Might be interesting to have it be IPv6 only - no need to waste IPv4 space with various nodes and whatnot, and it's a brand-new thing, you can skip all kinds of routing and port-mapping misery and whatnot by just starting out having it be IPv6 only. And who knows, maybe the built-in addressing and networking schemes in v6 might inform or modify how the addressing would work with this currency, too?