Both would be nice for different reasons. Lindos Mare is in a quieter spot but minutes in a taxi/bus from Lindos. Without a doubt it has a better beach than Ixia and plenty of nice beaches nearby.
Rodian Amathus is in Ixia. It's a popular resort though a bit dated and being on the breezier west coast is pebble beach. At the Amathus you'll have shops, bars, etc on your doorstep and at Lindos Mare everything is a walk or a 5 minute taxi ride away.
I'd prefer Lindos Mare as i prefer this coast but if you plan on using public transport, exploring Rhodes Town or taking boat trips the Amathus is the better choice.
With either hotel i'd go for B&B - there are so many great restaurants on the island it would be a shame to spend all the time dining at your hotel.

For the 3 week option i'd say if you could do 2 weeks at the Rodian Amathus exploring Rhodes Town, the west coast and doing all your boat trips then spend a week at Lindos Mare enjoying Lindos and the surrounding area that would be ideal.

Hi Marcus

Many many thanks for your input, it is really appreciated it only remains for us to make the decision then make the arrangements.

No doubt that will take some time, and things may change again, I may call upon your expertise again if thats o/k.

regards boaz

Hi Boaz

I love Rhodes. My fella and I have now been 6 times and never tire of it. We normally stay in Pefkos which is a lot quieter and normally go in September or October. Taxis and buses are cheap. We never go B&B or half board as the food is so cheap everywhere. If you stay in Pefkos I can recommend hiring a car from Marathon Cars in Pefkos or Georges in Lardos. Rhodes Town itself is fantastic especially at night. The old town within the walled city is fab. You can take a trip to Turkey from Rhodes harbour which is good for a trip especially if you want to buy jewellery or leather goods - if you go to Turkey make sure you get a price up front for a taxi and make sure they drop you straight to the centre and with no detours!! I find Pefkos is a good base for viewing the island by car. We always stay for a fortnight. People are the friendliest I've ever known and I've travelled quite a bit. Food is EXCELLENT all over!! Hope this helps, Nicky

Hi Nicky

Thanks alot for your info, you have given us more food for thought!!
We will now have to do a bit more research, but that only helps to form an overall picture of Rhodes.

Many thanks boaz