You can continue to use iWeb for your sites - iWeb is an application and will still work with both Snow Leopard and Lion, so you don't really need to change - it's only the alternative hosting that you'll really need to change.
Some alternatives are RapidWeaver - available from the Mac App Store. However, initially it might seem cheap, but be warned that it can become expensive as you have to purchase all the add ons and you can't start a site with a blank page, only a template.
Sandvox - also available in the Mac App store. You can try before you buy - download trial version of both RapidWeaver and Sandvox and see what they feel like.
Adobe Muse - something simpler that Adobe have created, so you don't have to purchase DreamWeaver. You can download the beta version for free from Adobe now and there are tutorials about how to use it.
Freeway Pro/Express - Freeway Express is available in the Mac App store, but the Pro version is a lot more expensive. You should be able to download a free trial version of this too.
Flux 3 - This is more advanced and has the ability to import html. You need a little more knowledge of html and css to use this, but you can go to the website and download a 30 trial version to see how you like it and there is a pdf quick start guide too as well as online video tutorials on their website.
Rages Software WebDesign - more advanced html editor.
PageSpinner - more advanced html editor.
There are then the online website creation packages such as Weebly at http://www.weebly.com and also Wix at http://www.wix.com where you can create a flash site and personalise it with a domain name if you wish. Also, take a look at WordPress at http://wordpress.com. This is initially free with your site being published on the WordPress servers, but you can upgrade to the Pro version if you wish where you can use your domain name. Alternatively, if you have a new host, then take a look at WordPress.org, that can be installed directly onto your server. WordPress is not just for making blogs, but makes good websites too, into which blog can be incorporated.
If you are purchasing new hosting, then it could be a good time to look into the Content Management Systems (CMS's) such as Drupal, Joomla and WordPress. These can be installed directly onto your server and you can create websites with this.
These seem to be most of the alternatives at present.