For days spent entirely in cities it is not likely you will get enough use to justify using a day of an interrail pass.
The pass is only valid on railways, this does not include large parts of the urban and suburban networks in most cities, for example London Underground, Paris Metro are not included.
Also not included are tram and bus networks.
Most cities will have day tickets or integrated fares for their local networks.
If you plan to travel
London to Paris
Paris to Stuttgart
Stuttgart to Vienna
Vienna to Berlin
Berlin to Copenhagen
Copenhagen to Oslo
that will be 6 travel days and will be covered by a global pass 7 days in a month if your first and last travel day not are more than a month apart.
Your post may be misleading us so I would like to point out the 2 options, a flexi pass and a continuous pass.
A Flexi pass allows you X travel days in Y months. These are best for a stop/start type trip where you travel longer distances and then stay in a town/city for a few days, using local transport options on a pay as you go basis. This is as described in the above post.
A continuous pass lets you use participating trains on any day within X days (or months) from your start date. These are more expensive to buy but allow a totally flexible approach to travelling in that time without the need to count travel days, so if you plan lots of days using your pass, for example basing yourself in a rail hub city (e,g, Frankfurt) and day tripping, then moving on to another for a few days.
Both of them are identical in the trains you can use and the need for reservations.
It depends from what you want to do and how you like to travel. If you want to see other places than aforementioned cities?
If you want to be very flexible (or less planned) and you just want to stay in the big cities but do daytrips and drop by the Alps, Black Forest, other natural areaus, to smaller towns and cities, the seaside,...? And Then I’lld suggest a monthly continuous pass for a month.
If you plan strictly and have a really good idea of what you want to do, then just count the days you’ll do the biggest distances on trains and choose a flexible pass according to the days you need :)