I'm aware of two Moskva kits, from Aurora and Airfix. The latter was quite a bit better, though the Aurora one was one of the firm's better efforts. Both of them are long out of production. I have no idea where to find either of them - other than the off-chance of finding them on e-bay. Maybe another forum member who's more up to speed on the modern warship end of things is aware of a source.
I believe Aoshima does a not-bad-but-not-great version of the Kiev on 1/700. There have also been several recent 1/350 Soviet warship kits from Trumpeter; I haven't kept the names straight.
If you're interested in resin kits, take a look at the huge range offered by the Russian company Kombrig. It covers most ships built by both Tsarist Russia and the Soviet Union. The company has been around for a few years, and the quality of its kits varies quite a bit. The earlier ones aren't as good as the most recent ones, which are close to the state of the art. The great feature of Combrig kits, though, is that, by the standards of resin kits, they're extremely reasonably priced. (The exchange rate for Russian currency probably has something to do with that.) You can get to the Kombrig online catalog by way of the Steel Navy website, <www.steelnavy.com>. That site also has a lengthy page of kit reviews, which may be able to steer you in the direction of the better kits.
Soviet warships in general make handsome models. I've always thought it ironic that two of the most ethically despicable governments of the twentieth century, Nazi Germany and Soviet Russia, built some of the best looking warships ever.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.