For chiang Mai the Suriwongse is simple comfort and convenient, and cheap, take a look at the central Duangtawan also and also the Amora ( previously Ridges ) as both convenient and well within your price range.
I like the Novotel but it is out of the center, so if you want central location try Central Duangtawan and Amora.

For Phuket you need first to choose 'which beach'. Although not a huge island it can still take 40 minutes or more from one location to another, so deciding whether you want very remote, remote, average or busy is important.
Another important factor when choosing where to stay on Phuket is whether 'absolute beachfront' is important or not. Some hotels and resorts are right on the beach so you walk from your room, thru the gardens to the beach, though many others are 'not' on the beach and you have to pack what you want for the beach, walk across a sometimes busy road to the beach, then head the trek all the way back everytime you want the bathroom or whatever, so deciding whether you want right on the beach or not is important.

Come back and tell us what sort of beach area you want and whther you need right on the beach and we can give more ideas and suggestions.