Here I'll try to write down list of typical activities that should be performed during web site launch. Please note that all of them have different priorities and impacts. And not all of them should be applied to your particular site.
In this file you need to specify what pages should be crawlable by web spiders. Please visit documentation site for more details. Basically you are specifying private (will not be available on Google and other search engines) and public URLs.
Configuring analytics will help you to have better understanding about visitors and content on your site: who visiting your site, how often, which mobile browser is the most popular among the visitors etc. Google analytics is the most well-known solution, but there are much more options, e.x. Mixpanel, KISSMetricks, Segment.io.
This file defines structure of your site. You should enumerate all pages that are available on your resource. Listing all pages will help web spiders (e.x. Google bot) faster index your content. See documentation for more details.
Setup Google Webmaster Tools - set of free tools to monitor and analyze your site. Easy to configure.
Setup social accounts if it's important to your site: twitter, google+, facebook, reddit.
Markup your pages with appropriate schemas from schema.org. This will help search engines to understand content on your site much better. E.x. if you are developing site for hotel use following schema - http://schema.org/Hotel, if it's blog post page - http://schema.org/BlogPosting.
Fill proper data in 'head' tag of your html pages. At leats don't forget to specify following meta tags: author, keywords, description.
Add favicon (icon that is visible in the tab of the browser). Read more about it.
If you are developing web app you may think about publishing it to Chrome Web Store. In such case you will have one more additional channel for discoverability - users will find your app through the store. It's fairly easy to publish application to Web Store. Please visit official documentation for details guide on this topic.
Before making your site public make sure to run PageSpeed Tools. You will get a lot of information and tips about performance on your new web resource.
Your site should have humans.txt file in the root which will provide information about people responsible for the site: developers, designers etc. Check out official documentation. If you will add such file guys from http://humanstxt.org will put link to your site in their directory.
Adding humans.txt file is not very common practice, but I like the idea and I think we should promote it.
There are a lot of ways how tow to make your web site better. You should optimize for speed, SEO, content, usability, discoverability and so on. Optimizations is an continious process. Everything can be improved and done better over time. In this post I tried to cover some basic steps that can be done very easily while publishing new site.