Either city is fine.

In TRV the Leela has a great seafront property and I'd highly recommend one of the villa rooms in the garden area as they have hammocks and verandas with chairs. This property is great for relaxation.They also have a great buffet by the pool in the main building. If your interest is the city and seeing that you are a Hilton Diamond, I'd highly recommend the Hilton Garden Inn close to many of the government offices. I've been always upgraded to their suite which is outstanding. In addition the property also has a great buffet. You'll be in the heart of the city and easy to get to shopping areas. I suspect that you'll want to be in the city as you'll probably want to spend most of your beach time in the Maldives.

Regarding COK the place I prefer is the Taj Malabar with a waterfront room, or alternatively the waterfront Le Méridien. At the Taj you are close to the Fort Kochi historic area, the spice market, the Chinese fishing nets, and the historic Jewish area. If your interest is shopping I'd recommend the Marriott adjacent to the Lulu mall.

I've stayed at each of these places multiple times and like them all and they all have great buffets.