There's a ton of options; I'm only recently getting into serious boardgaming (after a brief smattering of Catan back in university) and there's a vast myriad of choice out there.
However, if you're only on the outskirts right now, it's probably unwise to point you directly at something like Twilight Imperium, great though the game (apparently) is! When I went on holiday with my family last year (consisting of two grandparents in their sixties, my sister in her forties, and two nieces both under ten) I did quite a lot of investigation into what games I could find that would hit with such an audience who weren't experienced gamers; some were successful, others were not. They included:
Ticket to Ride: A predictable answer, but it was a massive, massive hit amongst the adults. Didn't quite try it with the kids; might regret that slightly in hindsight!
Kingdomino: A nice simple game with a decent overlay of strategy in terms of how turn order changes between turns. Queendomino is now out and pitched at gamers looking for more complex systems, that might be worth a look?
Incan Gold: A huge hit with everyone; it's a pure press-your-luck title but the tension works well.
Sushi Go: This made me realise one error of judgement; the children didn't quite get their heads around the scoring options; this was probably my fault, and a gentler lead-in might have helped, but they ended up with a bit too much to consider at any given time. Didn't really work.
Hey! That's My Fish!: Worked rather better; I perhaps should have explored the 'collect tiles' rather than the 'collect fish' variant (to encourage them to think more about territory control, but they seemed to enjoy it enough.
For Sale: The kids liked this a lot, and really took to the auction idea. They might have been a bit overly cagey as far as spending is concerned, but tended to play quite well. Family as a whole liked it too.
One thing I did notice in the context of this exploration was that the audience I was aiming for did seem to prefer games with simple individual decisions; For Sale's Bid/Pass in the first phase and card selection in the second; Incan Gold's Stay/Go. That might not suit you, necessarily, given you're looking from a Risk standpoint of having lots of choice at any given time.
