Regarding your table question- People generally choose divs over tables, BUT some things cannot be done well without tables. They still have their place. Divs and Tables inset within each other are often used for datagrid styled layouts for example. Often replacing tables with divs creates a nasty (oversized) amount of css code. If you can use divs cleanly, that is perfect. If it overbloats your code, then use the simpler cleaner old faithful table code - or combine them where it makes for better results.
More info on that here: Tables instead of DIVs (Joel Coehoorn's detailed answer: "The whole "Tables vs Divs" thing just barely misses the mark. It's not "table" or "div". It's about using semantic html.")
Regarding the topic of non-CSS since your question also refers to layout design formatting:
There are some things you cannot do well also without pure CSS, that in and of itself allows modern formats to work on multiple devices. This will reach more customers.
For newer layout types for sections of pages needing icons or photos, look into the use of inline-block styled lists. CSS does wonders with them. It is a nice third alternative.
For cross-device development, you should check out responsive and fluid formatting options. A good place to start is to look at http://html5boilerplate.com/ and also http://www.initializr.com/ (boilerplate and bootstrap).
If you haven't worked with them before, look into media queries for browser sizing and device orientation displays (landscape or portrait) - part of the fundamentals in responsive web development. You can then use your regular html within the constraints you set with these.