Depends on what you need, and possibly which devices will be moving around. But trying a quality extender is a great first step.
At our house in Canada, I already had a few wired points on the top two floors, and so replaced the router wifi (ie switched it off) with a group of Ubiquiti Access Points… I probably have way too many now but coverage is excellent. This hw system can be used as a mesh (ie some AP using a wifi backhaul), but in my case all AP have wired backhaul (which is the best / fastest / most reliable but most complex if you need to add any wiring… like I said, I had three wires installed already, plus the main router in the basement).
Here at our apartment (my wife works abroad), the situation is closer to what you describe: good coverage from the router wifi itself in most spots but the main bedroom is far from the router, around a corner, and with multiple walls (from the en suite), etc., and no signal in about half the room.
Noting that there is a handy electric outlet right at the corner, with line of sight to the router and into the bedroom, I bought a TPLink wireless extender. Probably over-spent at 100€, but went for what appears to be their top-of-line model: RE655. It plugs in to the wall, has a discrete look with fancy antennas, is easy to install and program.
If you use the existing SSID and password for the wifi being extended, things like iPhones and iPads will move seamlessly to the stronger signal (perhaps with a slight hiccup, eg walking into bedroom while on a FaceTime call). You don’t need mesh for this functionality with anything more modern than say an iPhone 5 (I don’t know exactly when this was added, but it’s been ages). Static things, like a laptop on a desk or a MuSi Qb simply don’t care: they see a strong wifi and connect.
The reason I got the RE655 rather than the equivalent-but-lots-cheaper RE650 is its mesh capability. If things hadn’t worked as I hoped, I could buy a second one, wire it in right at the router, switch off the router wifi, and use the two APs as a mesh network (the original one has no possibility of a wired backhaul). In retrospect, I should have started with the much cheaper version and “traded up” if I needed mesh capability after all. Oh well, lesson learned!
Bottom line: buy a good, modern high-throughput wifi extender model; set it up with your existing SSID and password for both bands; put it as close to the corner / mid-point between the router and the dead spot as you can. You’ll get better than 50% of your router’s direct wifi speed, and it will be very reliable. Get it from somewhere you can return and upgrade if it doesn’t do what you want and you need a more complicated solution. Avoid the 20€ models, they are way too slow for your modern expectation of speed and performance.