We both agreed it would be unfair for such a big dog to be stuck in a 2nd floor apartment.
The physical size of the dog doesn't really matter for apartment living, to be very honest. For example, I think a Newf would be much better suited to an apartment than a Boxer or a Lab, both of which are known to be high energy. Every dog needs exercise, and the size of their living space if they're properly exercised is pretty unimportant (for the most part).
~ a breed that's know to be easy in the house training department
This is very much an individual thing and is not breed dependent. Most puppies aren't going to be reliable with potty training until around six months of age. This is true for dogs from the size of Chihuahuas to dogs the size of Great Danes. For example, my Great Dane puppy had to go outside every 20 minutes while active until he was almost six months of age. Other people's Danes are much easier than that. If you're potty training in a second floor apartment, expect it to be a challenge no matter what breed you choose.
~ good with kids (trust me we live in an area with lots of little ones so he/she will be well socialized)
A puppy of any breed is going to be mouthy for several months, at least. No puppies are automatically good with kids. It takes time, patience and training to teach bite inhibition.
~ we go for long walks every Sunday (like 4miles since we both have off) so need a dog with energy but not a super high amount of it. We also go on many daily walks.
No puppy is going to be able to walk 4 miles right off the bat. Forced repeated exercise isn't recommended for puppies of any size. By "forced repeated exercise" I mean walking or jogging at the same pace for an extended period of time. Puppies need to free exercise and move at their own pace (preferably on a softer surface like grass) until their growth plates are fully closed.
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Some generalized comments:
It honestly sounds like you want an adult dog. "Easy to potty train", "good with kids", "we walk 4 miles on the weekends"... Those are all adult dog qualities, and you're going to have to be patient and wait a while for a puppy to mature before it's capable of doing any of those things.
I do think a giant breed like a Newf or Bernese Mountain Dog fits your criteria pretty well. That being said, expect to pay $1,500-$2,500 for a well bred puppy of either of those breeds. It's very important to buy from a breeder who does all of the health testing for these breeds, and if you don't, you're setting yourself up for an increased risk of a dog who doesn't live past the age of 7.
Another thing to consider is the stairs in your apartment. A few different studies have shown that going up and down flights of stairs increases a puppy's risk of hip dysplasia significantly. It would be highly advisable to carry your puppy in and out until he/she is at least 4-5 months of age. With a giant breed, this means you'll be lugging a 50-60 lb puppy outside in your arms. Are you capable of doing that?
And the big thing I always like to warn people about with giants is finances. Everything is more expensive with a giant breed. My Dane puppy ate 10 cups of food a day while he was growing, which resulted in my food bills being $160 a month. You don't want to alter a giant breed before growth plate closure (meaning you'll have to deal with at least one heat in a female), which increases the cost of their s/n significantly because anesthesia is based on weight. You're likely going to pay $500-$1,000 for a s/n for a giant breed dog depending on prices in your area. These breeds are also prone to bloat, and if your dog bloats with torsion, surgery will be required to save your dog's life. A GDV surgery can run anywhere from $3,500-$5,000, money that you'll need to come up with at the drop of a hat.
Due to these issues, I have my dogs insured, which costs $65 per dog per month. I imagine the price would be slightly less for slightly less expensive breeds like Newfs or Berners.
If you can accommodate these things, then either of those breeds fits all of your criteria pretty much perfectly.
