Great choices, I just did them all recently except Stockholm (which I visited a long time ago and was the least favorite).
Depending on flights, I’d do Helsinki - Copenhagen. Nordic cuisine in both places is off the charts (probably true of Stockholm too). Very easy to get from Helsinki-Copenhagen on Finnair (cheap BA award).
Helsinki can be covered in two days but taking the Ferry to Tallinn in Estonia is a nice day trip.
Stockholm is one of the best food/wine cities in the world right now. Helsinki is a nice city, but small. I’d do that as it will likely be easier to do a stopover in Amsterdam on a future trip.
Is it mainly a food and wine trip or are you also looking for museums, sights in general etc.?
I live in Copenhagen, have lived in Amsterdam and been to Stockholm twice and think all three cities are worth experiencing. Never been to Helsinki. I would also limit myself to two cities during this trip and then return another time. Late May is normally a great time to visit - mild weather and long evenings (sunset at around 9.30 pm).
If you’re not in art museums I would skip Amsterdam on this trip. In Stockholm you should make sure to visit the Vasa Museum where they have a full size 17th century warship on display: Vasa History
I will get back to you later with tips for restaurants and good bars in Copenhagen.
We’ve stayed at the Hotel Diplomat in Stockholm. On the water, excellent location, Dux beds, and not overly expensive. Definitely ask for a waterfront room
Don’t know what kind of food you are looking for, but had a great dinner with my tasting group at AOC last year (Home) It is an expensive restautant (** michelin starts) but the food, service and atmosphere was fantastic.
You also have some nice wine bars in town. I really like Casa d’Antino (http://www.casadantino.dk) which is an Italian restautant but also a wine bar. Very good italian food and a beautiful selection of wines. Normally also quite a few interesting wines by the glass.
Ved Stranden 10 is very popular and right in the centre of town (http://www.vedstranden10.dk). Has outdoor service in the Summer.
If you’re up for trying organic and quite different pizzas, and great cocktails, you should try the restaurant Neighbourhood (http://neighbourhood.dk).
And of course you should spend some hours eating and drinking at the food market, Torvehallerne (https://torvehallernekbh.dk).
I just got back from a short trip to Copenhagen last week.
If you are looking for clean & very affordable lodging, the Wakeup Borgergade fits the bill (I spent 3 nights for under $300). It is not luxury but I was very comfortable. https://www.wakeupcopenhagen.com/the-hotels/copenhagen/borgergade
Great location, walkable, across from Pluto and Gasoline Grill.
They are closing to head down for their April - May pop-up in Mexico - noma
108 Restaurant is worth a stop. It is a more casual restaurant from the noma team - https://108.dk/welcome/ I think this will remain open during that time.