I think my choice would depend on a few things such as the age of your kids, and how many people you were hoping to have play at once.
I grew up with Mario games - starting on the NES with Super Mario Bros and progressing through many systems and Mario games since then.
I'd recommend Super Mario Kart Wii, though I will note that I've never actually played Super Mario Galaxy, so I can't personally compare it. I have probably spent more time playing all of the different Mario Kart games through the years than any other game, so I lean towards it. It's a personal decision though, and you do have to like the idea of a cartoon racing game to enjoy it. The Mario Kart games are classic. Great for multiple ages to play together, and just so much fun. It's easy enough for everyone to learn, but really challenging to beat the entire game.
On the Wii, Mario Kart can be played simultaneously by 1-4 players using a split screen so it's a great game to play together. With the "items" you thow at each other, it keeps it really competitive and it's anyone's win until the end. Since it's a racing game, I find that there's excellent re-play value (i.e. you're always trying to do the same tracks again to improve your time, and unlock new items etc.). It takes quite a long time to unlock everything available, so it keeps it challenging and exciting. There's 50, 100 and 150cc (increasing speed and difficulty) so there's a range of levels for everyone to compete. And once you've won every course on the 150 level, the game unlocks "Mirror Mode" where now you can race the courses in the reverse direction. (Just when you've memorized every turn and trick on the course, it's like a whole new track going the other way!)
However - to be fair, as I mentioned, I haven't played Super Mario Galaxy. And - I should point out that Galaxy is overall the TOP rated game available for the Wii of all games. Metacritic.com ranks games by averaging multiple reviews from other sites, and Super Mario Galaxy comes out as the #1 game overall with an average score of 97%! So - it must be excellent. And, I do actually own it, I just haven't gotten around to playing it yet, LOL. It does look like a fantastic game based on the reviews. (Note that it's only a 1-2 player game if that matters.)
For comparison, Metacritic lists Mario Kart Wii as the 27th Wii game overall, with an average review of 82% over all the sites.
I will also point out that Mario Party 8 is rated as only the 208th Wii game overall, with an average score of 62%. I haven't played it for the Wii, but I have played some of the other Mario Party games and I could never get into them. I'm thinking that it might be more appealing to younger kids. I own one of the Mario Party games for the Gamecube, and I only ever played it once or twice before it sat in the drawer. I would agree with the 62% and 208th spot ranking.
Something else to consider is buying some of the older Mario games with Nintendo points, if you have your Wii hooked up to the internet to access the Virtual Console. The NES games are only 500 points (roughly worth $5 US), Super Nintendo games can be purchased for 800 points (roughly costing $8 US). You can download some of the older games directly to your console. I'd recommend Super Mario World from the SNES, Super Mario Kart from the SNES. If you wanted to try a Mario Party game, I'm sure there's some likely available. You don't get the "Wii" functionality with the controllers, but you can see what kinds of games your kids are most interested in, and it's an inexpensive way to grow your collection of games. (Be aware that although you can use the Wii controller directly for original NES games that you either need the "classic" controller or a Game Cube controller for the SNES games and above since you need the extra buttons that those systems used.)
Let us know when your family has become the newest fan of the Mario Kart games, LOL.

Warning - it's addictive, LOL!