Any codecs or anything like that seem like a screamingly good target.
Right now they're one of our most egregious sources of security vulnerabilities (mostly due to a lot of hands-on bit-twiddling that results in a lot of possibilities for overflow). It's gotten bad enough that a number of system developers (browsers, OSes) have been shifting to a model where codecs are strictly sandboxed, and just get a single binary input blob, and a single output blob, and don't get any other kind of access to the system they're on - it's a scorched earth problem, but it really is that bad.
The thing about trying to write one with Rust is, if you actually 'went with the flow of the language' and didn't just immediately pop into `unsafe`, you'd be able to write a really safe codec.
-but-
The real payoff is that the performance would be surprisingly good - usually a suggestion like the one I just made would absolutely wreck performance, but one of the big things about Rust is that because it lets you describe what your intent is as a programmer in such higher-level terms (despite being a machine-level language), it gives the compiler a lot more information about the scope of your intent, which opens the floodgates to potential optimizations.
For a really easy example - Rust does all variables as "immutable by default". When you're programming in C, and something is compiling your code, there are tons of opportunities where you'd go "oh, well we already calculated this, why don't we just cache it?" But the compiler can't, because it doesn't actually know what you, the human, know - that that thing won't change. Because that knowledge is available to the compiler through Rust, the compiler actually DOES know, so tons of things can get inlined, cached, and otherwise optimized for you which you'd otherwise have to do by hand.
Usually when people do these sorts of things by hand, they'll ace a couple key optimizations (usually things that show up in profiling hotspots) and completely overlook hundreds, even thousands of other potential optimizations.
There are tons of other "high level intent" things that give the compiler more info it can use to optimize, but the "immutability by default" one is a really easy one to explain.