I saw an interesting article in the papers today about doing some tourism development in the northern part of the country, near the town of Al-Ruwais.
I've been up there a few times and they are right -- there is very little in the way of infrastructure development for tourists.
The only restaurants I found in the town were a couple of small hole-in-the-wall “cafeterias”. If there are any reasonable restaurants up there I couldn't find them. I always advised people to bring food with them or plan to drive back to Al Khor if they want to go to a restaurant.
I did mention in my post “What to Do in Qatar” about seeing what I think are the coolest things up there, the abandoned villages between Al-Shamal and Fort Zubara. They are interesting and worth a look, especially if you have a four-wheel drive as some of the nicer ones are off-road a ways, by the coast.
Fort Zubara by itself is not all that exciting but since it's near the villages it's worthwhile stopping by.
The article doesn't mention there are a few other old forts up around there that could also be utilized for tourists.
As for archaeological digs I attended one once with the Qatar National History Group but there isn't much there for your average tourist to see, just some outlines of where some houses once were and some tiny shards of pottery. It’s not Petra or Ephesus. Qatar did not have a huge historical civilization occupying the land, the inhabitants were, at most, a few thousand fishermen and Bedouins. There are no ancient monuments like you would find in the Levant or Iraq.
The article mentions “breathtaking views of a conventional desert” but I think they are confusing it with Southern Qatar.
As for the rock carvings at Al Jassassiya while interesting I don't think they are much in-and-of themselves for most tourists to take the journey to see them.
But the article misses something else near to the carvings, the beach at Fuwarit, which has been a favorite of many ex-pats looking for an out-of-Doha getaway. I've haven't been there for a couple of years but I know some people who go there at least once or twice a month to relax on the beach (maybe I'll go sometime in the next couple of weeks and see how it looks). Qatar could think of developing that a bit, it doesn't have to be anything fancy like Sealine Resort but a couple of restaurants or a small hotel would be good.
At least if they develop Northern Qatar they might clean up the shoreline!