Can anyone offer any recommendations on any accessible war games - other than Risk. I've looked around previously and it seems that most are incredibly complex and/or require a tremendous amount of time to play.
Diplomacy's either a much better or much worse alternative to Risk. Depends who you ask. Not directly comparable but scratches the same itch, possibly better (see: depends who you ask).
The Board Game Geek site probably has some lists for semi-casual or otherwise less-hardcore wargames. That'd be the place to look. Then see whether Shut Up & Sit Down has done a video review of any that look interesting to you, before buying (they have for Memoir '44, IIRC).
The rules are pretty elegant and fun, and are quick to teach and play. A game usually runs 30 minutes to an hour. Miniature wargaming is always going to be a bigger investment in money and effort than a board game, but DBA is pretty easy to get into: you only need a couple dozen figurines for an army, and a playing surface of about two or three feet square.
The central conceit of the rules is that the important thing is modeling a unit's role on the battlefield, and the rest can be abstracted away. So for example a unit of pikemen is a unit of pikemen, whether they're a Macedonian phalanx or a Swiss landsknecht. This lets the same set of rules support battles from the bronze age to the renaissance.
And so, we'd have a gaggle of people merrily running around the town, trying to scoop up supplies and whatnot, as things got more and more chaotic. Always a blast.
I think the ColdWar Commander / Blitzkrieg Commander games can be picked up in that time. Movement, command, and combat rules are quick and intuitive, and it generally lends itself to a "resolve-problem-by-common-sense" approach. It's great for casual gaming.
http://backtominnesota.com/Ancients%20Old/Old%20Ancients.htm
(Or my all-in-one file, here: http://suspended-chord.info/static/downloads/paperparachute-...)
The tutorial in the Twilight Struggle app is a good, fast-ish, introduction to the game.
Neuroshima Hex! Is one of the greatest games of all time, but it’s more of an abstract than a what people think of as a wargame. You build competing programs (Armies) that execute during battles.