Staying near Gare du Nord, Paris

If you've never visited Paris before, stay in the rue Monge area, which is in the Latin Quarter, btw. The area around the GdN is a safe enough area to stay, though gritty and not charming at all.

If you're near the RER B, you'll be able to get to the airport easily.

The GDN neighborhood isn't very pleasant or convenient to anything except the station and RER. Place Monge is a nice neighborhood with a Metro station and another one (Jussieu) nearby. A more convenient choice would be somewhere on the RER B line, which serves both Gare du Nord and CDG. Stations on the left bank include Denfert-Rochereau, Port-Royal, Luxembourg, and St-Michel. Generally, closer to the river = more expensive.

Place Monge is unquestionably far, far better than Gare du Nord for a visitor. It is pleasantly quaint, with a very good market on Wed, Fri and Sun, and metro line 7 is convenient to many attractions (Louvre, Opéra, southern half of Marais).

We just returned from 2 weeks in France. We spent the first 3 nights in the Latin Quarter, on Rue Monge (Hotel des Nations Saint Germain) the hotel was fine, nothing special but the location was great, 3 minute walk in either direction to subway stops, and very close to place monge for the outdoor market. There's also a bus route along the street. As others have said the Latin Quarter is a great area to stay in, charming, walkable, plenty of locals, taking their children to school in the morning, etc. At the end of our trip we stayed 3 nights closer to Gard du Nord and Gard L'Est, at Hôtel Littéraire Arthur Rimbaud, a Best Western collection hotel. This neighborhood was fine, safe, with plenty of restaurants, a subway stop very nearby etc, but definitely lacked the character of the Latin Quarter. It was a 15 minute walk to Gard du Nord, where my daughter caught the train to CDG on departure morning. We opted for a taxi to the airport the next day (bolt app, 8:30am on a Tuesday, ~27 euro).
Overall, I would choose the Latin Quarter over the 10th, but one big thing to consider - we had someone in our group who had mobility issues - he couldn't go upstairs, and many, if not most subway stations didn't have working elevators or escalators. Even those that did, if you're switching between lines, stairs will be involved between platforms. Neither subway station on Rue Monge had an escalator. The Château d'Eau subway station near the Best Western did have an escalator.

For anyone with mobility issues, taking a bus rather than the métro is a must.
The bus system in Paris is excellent.
And a benefit of a bus is you can see Paris as you go.
I use GoogleMaps in Paris which tells you how to get from Point A to Point B by bus, métro, car or walking. Supremely useful.

I am not a fan of the Gare du Nord area and agree with others that the Latin Quarter (6th arrondissement) is better.
Still not my favorite, but better.

The bus is definitely a better option for mobility issues. I had mapped out an evening bus tour (Route 56 to Route 69 to the Eiffel Tower) but unfortunately the walk to the bus stop seemed daunting at the time for my husband.
Does anyone know if you get a free transfer between buses and/or subway to bus? One day we took the subway, then a bus to get as close as possible to Sacre Coeur. I assumed we wouldn't be charged for the bus, because it was a transfer (within about 15 minutes of first tapping into the subway station using the navigo card loaded with 10 rides). But it appears that we were charged for another ride when we tapped onto the bus.

"Does anyone know if you get a free transfer between buses and/or subway to bus? "
There is no free transfer between buses/trams and the metro. There are free transfers between buses and between trams and between buses and trams.