I can't give you an
SEO perspective on that site and those links, because I'm not an
SEO expert. I can, however, give you a usability and accessibility perspective.
For the main page - those lines at the bottom should be redesigned to look like the news briefs and sales pitches they are. Why not create another section below that image on the main page just to push the things that will get people in the site beyond the front page?
For the sub pages:
I don't think the problem is having the links at the bottom. In fact, it's usually easier on the user if they have more than one way to get to a page. It's particularly nice to have links at the bottom when there is page scroll. However, there is an altogether different problem with the links at the bottom of this page. There are too many, and the contrast is just terrible for reading. Three rows of page menu is way too much, it shouldn't have to be more than one across.
That's not just a problem with the bottom links though. Here are my visual impressions of the sidebar links:
1) Way too small in proportion to the rest of the page. The navigation should be prominent and.
2) The text is too small and the menu items are too crammed together - add some padding to separate them and make the more easy to read.
3) There are, again, WAY too many links. That needs to be consolidated because it's just too overwhelming. For instance, why are 'Meetings and Events' and 'Weddings' two separate menu items? I'd consolidate that into 'Events' with two subsections, one that is 'Meetings' and one that is 'Weddings' but I'd also put 'Calendar of Events' in that section. Similarly with 'Things to do', 'Spa,' and 'Golf' - they could all be together. The same with 'Take a Tour,' 'Photo Gallery,' and 'Interactive Map.' You get the idea.
So, that said - I think the site would benefit HUGELY from a lot more consolidating of those menu items and making them more prominent and readable.
On another note, I'd definitely say keep the text footer links for accessibility sake while your sidebar submenus continue to be reliant on Javascript. But like I said, I like the links at the bottom anyway - makes it easy to pick where you want to go when you are at the bottom of reading a page.
My last thing on this - If you want your client to 'modernize' and do things that are 'in' with their website, why not start by suggesting a 'modernization' of the code behind that site? I had flashbacks looking at it.