I have searched up and down throughout the internet and cannot find out how much a Miyata Omnium is worth. It's in good shape but needs a new seat and tires. I know it was offered for one year but what are these worth? The guy wants $350. Worth it or should I keep looking? I am new to older bikes and the whole vintage scene so any help is appreciated.

The Omnium orignally sold for $800 US. Whether it is a good buy will depend greatly on your local market. In a big and typically expensive market, this would be a good buy. In a small market, not so great.

The other thing to consider is, what kind of a bicycle are you looking for? The Omnium had relatively slack geometry and a long wheelbase and rides rather like a sports/touring model. It's great if you like cushy rides, but not so great if you like stiff, efficient bicycles. On the plus side, it has good components, with a New Shimano 600EX group and is fairly light, at 22.8 lbs (for the 57cm size).