You're anxious arriving at a new destination. Don't worry, I'll explain how I get situated and started in every new place I visit.
Believe it or not, I'm not a huge fan of big cities. There are some big cities I enjoy such as Denver, Bangkok, Copenhagen, and a few others. However cities like New York, Paris, and Barcelona aren't usually my scene. But my opinions on cities are 1. Not totally based on size and 2. Irrelevant to you, because your travel preferences are not going to be the exact same as mine. Luckily, you can learn to navigate and feel comfortable in any city no matter what size.
The first thing I do when I get to a new destination is obviously check in to my accommodation. This is usually a hostel but every now and then I will stay in an Airbnb. Most hostels won’t start checkin until around 2 pm. Some places don't actually mind and others are sticklers about it. Either way there should be a room for you to put your luggage in if you do arrive early. Once I no longer have my bags I go walk around for an hour or two. I never ask for suggestions on my first time out because I like to see what I can find for myself. I almost never go inside anywhere and I kinda just wander. If you also are someone who likes to count their steps, you'll hit 10,000 easily everyday. I'll walk around and mentally take note of any places that seem interesting enough to come back to. The only time I will go inside somewhere is if I need some food. Although with my wandering, I can usually find a market, some street food, or a local grocery to get something light. Try to keep note of how the streets are laid out and how the city is organized. In small cities, it’s easy because there’s not that much to remember. In big cities, it’s easy because they almost all have a grid layout. It’s the medium sized cities that can be a bit tricky. Without a huge metropolitan, medium sized cities have more freedom to design layouts in more unique ways, mainly due to the lack of cars. Don't let this turn you off to medium cities, as I find them to be the best in terms of culture and things to do. One thing that many cities have in common (no matter the size) is they have a center to which all roads point towards. There’s a reason the phrase is "All roads lead to Rome."
Once I've had my fill of walking around and I feel like I have a good sense of my surroundings (or if it’s summer and I get too sweaty) I go back to my hostel to shower. Unless you’re going out to dinner or a bar after you arrive in your destination, it’s best to wait. I know it feels gross getting off a train and not going to shower immediately but you’re gonna get gross walking around all day so you might as well not dirty more of your clothes. Afterwards is when I start talking to people about things to do and recommendations. Most hostels have tons of pamphlets and brochures of things to do including tours, outdoor activities, and shopping areas. Many of them also have dinners out or pub crawls. So as long as you don't drink too much, you can remember what you see around you while you’re with other people.
While you can always lookup things to do online, many places list very touristy and very expensive options. Websites like Trip Advisor as well as booking service websites often get commission and thus push certain activities. If you are looking for recommendations online, read travel blogs or find Youtube videos with maybe not as many views. The less monetized these sources are, the better chance of the activities being worth it. One of the best ways to find activities is to simply talk to locals. They will now the best and cheapest options for all types of things around the city as well as directions to get there.
Another great way to learn your way around a city is by utilizing public transportation. Subways, trams, buses, and other forms of public transport all offer routes around the city. Understanding the direction of transport routes can help ingrain a mental map in your head. While I usually won't wander far enough to use public transport the day I arrive in a city, I tend to use it almost every other day and it will help you gain a better understanding of the city layout as a whole.
Some other ways to help you get comfortable and navigate a new city are:
Download a map of the city on Google Maps app (no data requited)
Figure out which streets are main roads
Learn to figure out East, West, North, and South using the sun/shadows
Walk around with someone who has been there for a little while
Find plazas, monuments, and other not worthy locations
Mentally (or I guess you could write them down) create reference points around the city like breadcrumbs
If you should take anything out of this it’s that with a little effort, you'll be able to find your way around anywhere. Except for Venice, it’s a nightmare even for me. But aside from that, you can learn to navigate even the most medium sized cities. If I'm being honest though, you may have a better time if you don't know where you are and where you're going. Being "lost" is half the fun.