There is something from Pompeii
http://www.thelocal.it/20160802/refurbished-pompeii-kitchens-show-how-ancient-romans-cooked , and a fair number of modern books on Roman cooking will have stuff about the kitchen and how it was organised - this one does:
https://www.amazon.co.uk/Around-Rom...F8&qid=1485553367&sr=1-15&keywords=roman+food (I've been meaning to write something about Roman food and drink for a long time, so I have a collection of such books).
Food was important to the Romans - and showing off your wealth and sophistication by having your guests taste amazing meals was, as always, important. Cooks were often slaves, but it was a skill, and so getting someone talented was something to be proud of.
I suspect that higher class citizens wouldn't go much into the kitchen, but they'd make sure that it was well run, in exactly the same way you dont see the family wandering down to the kitchen much in Upstairs Downstairs, but they'll want the meals done properly.
On the other hand, most people cooked their own food, but since the bulk of the Empire's population was still rural, it was relatively easy to obtain supplies. For places like Rome, you had large bakers, daily markets, etc. And you could just get a snack on the way - there was a type of pizza thing (but no tomato's!), with toppings. which you'd much while having a drink of wine in a bar.
There are loads of sites for supplies if you want to reenact a roman kitchen - knives, ironwork, pots and mortaria are all available
http://www.trinitycourtpotteries.co.uk/1Roman Replicas.htm (mortaria turn up all over the Empire, they are like the Kenwood Chief, because you know when somewhere has become Romanised enough for someone to say 'I want one of those' - there even one found in mid Scotland).
https://www.armamentaria.com/store/...dex&cPath=43&zenid=058boofsunppsiec8r3rfbgnt1
I'm sure there must be some journal articles about Roman kitchens and the status of cooks - Google scholar would be a good place to search, and the JRS a reasonable starting point.