It really depends on what type of website you have.
iWeb and similar apps are probably OK for the "standard" website with text and images. If your website includes other media such as movies and music, you need to work a little harder. Displaying these using the QuickTime plugin was never the answer and, nowadays, neither is flash. YouTube (and its far superior rival Vimeo) seems to be the easy answer and, it probably is if you want your site to look like a zillion others.
Online site builders, like the much touted Weebly, don't provide the answer either. Weebly uses the standalone version of the Wordpress mp3 player and an ancient version of the JWLongtail video player. Both are way out of date and won't function on most portable devices. Far from being free, except in their most mundane form, this method of site creation is a lot less versatile than using applications such as iWeb and will end up a lot more costly in the long run.
A lot of the emails I get are from musicians who use HostBaby wanting to change to iWeb. The main reasons being the high cost of a HostBaby site and the lack of ability to produce a unique design.
Having looked "under the hood" of some of the designs that claim to be suitable for all devices, I'm not impressed. On the other hand, if you create a version of your site suitable for cell phones using the available online resources, your going to have to accept their almost non existent ability to play media.
Right now, I wouldn't recommend any direct replacement for iWeb. As I mentioned previously, why replace iWeb with something that's equally redundant such as SandVox and RapidWeaver or the hopelessly antiquated Freeway? Ask your self why Apple is quitting on iWeb. It would make an interesting topic in this forum!
Making the move to code entry style software is not as difficult as it appears to be. Most of the so called professional designs out there are built from "templates" in the form of stock CSS stylesheets. Modifying them is a no brainer compared with trying to produce a template for an app like iWeb. Most of the code entry style software is WYSIWYG and, the better ones, show the changes in real time.
If you want to stick with drag and drop, you'll need to wait for the next big thing. You don't need to change but the problem is that standing still is equivalent to going backwards!