I've seen better odds of Theft/Heists missions on systems with mixed allegiances (Federal, Imperial, Alliance and Independent). When it's a single one or majority of the same (specially if factions on same alliance hold majority of settlements), odds seem to decline as they don't tend to hit each other as often (they still do sometimes). Close by systems can also have missions targeting the system you want to hit, usually within 15 ly (I've seen at most 12 ly I think), so looking nearby can help, but keep in mind distance to arriving star when using nearby systems.
On Inara, you can look up nearest stations and filter "Station Type" by "Odyssey Settlements". This will only return valid Odyssey Settlements, and they'll end up grouped by system if you leave the sorting to ly distance to yourself, and that can help you find systems with lots of settlements. Then you can check the distance to star, and that gives you an idea of how spread the settlements are inside the system. Keep in mind that large distance to star isn't necessarily bad, what is bad is if there are several planets distant between each other, meaning longer travel times. If a system has a planet with moons that are very populated and a station near them, even if they are 5 kls from star, you still get good mission opportunities from there.
For example, near me, Heheng has the most Odyssey settlements, with a variety of allegiances (mostly Alliance, some Independent, one Federation), and all of them are grouped within 2.4 kls (but not a lot of exact matches, meaning most likely several moons with a couple settlements each, which a quick check to EDDB confirmed). This system could be good, but there are better matches.
Unless someone writes a specific search mode that scores systems by weighting settlement density against distance to nearest station in the system, finding good systems for Odyssey stuff is still kinda hard, since Inara limits the number of hits on searches (and searching for settlements finds each individual settlement as a hit). Or if when searching for Systems there was a column for number of Settlements in the system.
I'm not sure if War/Civil War/Elections states affect availability of Heists/Thefts, only that Restore are common only on factions under either Pirate Attack or Infrastructure Failing. I think I've seen them on Bust, but don't count on it. Still, I guess that Elections/War/Civil War might affect availability of these missions, since it makes sense for them to undercut each other using outside contractors.
I'm currently on Quator, and I'm getting quite a few opportunities for Heists and Thefts (3 Empire factions, 2 Alliance and 2 Independent, but only Alliance and Empire have settlements active, 3 Empire Settlements and 2 Alliance Settlements). Board shows right now 10 Illegal Procurement missions out of 54 missions total: one Covert Theft, one Theft, one Heist, one Non-violent Heist, and the rest spread into Espionage variants, with one person asking for a delivery of Push so they can endure their daily shift. There was a War recently, and I didn't see a difference between Heist/Theft availability, but one person seeing a mission board not so often doesn't make statistics. Would probably be better for more Theft/Heists if there was more settlements to generate more missions, or if there was elections going on (assuming they actually affect Heist/Theft availability).
