Out of those hotels, I definitely recommend Century Southern Tower and Tokyu Excel. CST is in a great spot with possibly an awesome view. It's my favorite hotel in Shinjuku. Tokyu Excel is possibly the best-located hotel in Shibuya. Given the price difference, maybe go with CST.

For the most part, Shibuya and Shinjuku are very similar in terms of transportation convenience, especially if you're talking NRT and bullet train (which you'll catch either in Tokyo or Shinagawa).

You (OP) say you're not looking to shop, but I am sure you'll end up shopping nonetheless. Both Shinjuku and Shibuya are great for that, but Shinjuku has more of the mega-stores. CST is right across from Times Square Takashimaya which is adjoined by huge bookstore and a huge Tokyu Hands store.

Restaurants - basically a toss-up between the two areas. Unlimited options in either place.

Nightlife - both have plenty of nightlife, although I favor Shibuya for that. I admit I'm not up to date on the nightlife since getting married. Shibuya is more for the younger crowd, but (as someone else said) I do think Shibuya is changing. More of Shibuya is more buzzing into the wee hours. Just a whole bunch of cafes, bars and izakayas open late. East side of Shinjuku has that, too, but I find the nightspots in Shibuya to be less intimidating.