Going out for a run when you first arrive in a certain place can be a quick and fun way to orient yourself, I have tried it several times: you avoid the queues for bus and train tickets, you have the possibility to discover some hidden gems outside the main arteries and tourist routes. In case of jet lag, take the opportunity to get out early and enjoy the city almost exclusively (and maybe take a nap on your way back).
Of course, care must be taken not to get lost and above all not to accidentally end up in the ‘wrong’ neighborhood, especially if you run alone, but with a little planning and a mobile phone you will find beautiful running routes wherever you are traveling.
The phone can be very useful for running around town, I use the heatmap of the Strava app, which highlights the routes most used by thousands of regular runners in a given area: if a route looks appealing on the map, but none on Strava runs there, it is probably best avoided.
The locals can also be a very useful help: whether they are groups of local runners that you can easily find on social networks or the manager of the structure where you are staying, in general they are all happy to give indications regarding the most popular and suitable routes.
Also don’t forget that many cities now offer paid tours for running. Just show up at the appointment to run with a local expert. Afterwards you will probably be taken to dinner or an aperitif: an original way to get to know a city. To find a tour, search for the location where you are staying on Google or at the tourist information centers of the destination (also on social networks).
Keep Run!