Specifically wondering if we should avoid alcohol for the first few days as we have had issues with altitude in New Mexico and Colorado at 13,000 feet.
I suggest consulting a qualified medical professional to ensure you take precautions appropriate for you and your personal medical situation. Avoiding alcohol is one way to mitigate it, but may need different remedies if you are particularly sensitive to elevation changes.
Don't worry the altitudes are no where near what you would see in the rockies.
The only way you will see 13,000 ft is of you go to the Jungfraujoch or Klein Matterhorn at Zermatt. Sleeping in Muerren or Zermatt is the same elevation as downtown Denver. Even the top of Schilthorn is barely 10,000 ft.
First, thank you for showing your location in your profile. It helps to know the altitude you are used to.
I was on the ski patrol at Loveland ski area in Colorado for five years. We were told about the classic case of altitude sickness being the lowlanders who came to Colorado to ski. They drove all night to get here, not getting enough sleep and probably drinking in the car on the way. Then, they stopped at Loveland because it was the first ski area they came to. Unfortunately it's probably the highest ski area (average elevation; the base starts at about 10,600 feet). The parking lot is higher than the top of the Zugspitze). The slopes go up to over 12,000 ft. By noon they are in the patrol room barfing their guts out.
I used to live in Pittsburgh (elevation about 800 feet) and a few times came out to Aspen (elevation around 8,000 feet). I generally had a few glasses of wine with dinner without a problem. Some of the lifts there go up over 12,000 feet.
Although the Alps are about as high as the Rockies, you will probably be staying in towns that are not that high.
Innsbruck is about 2000 ft.
Alpe di Siusi, in the dolomites, is at 1850 feet.
Garmisch-Partenkirchen is at 2300 feet.
Füssen is about 2650 feet
The town of Lauterbrunnen is at 2600 feet; Mürren is at 5400 feet.
The town of Chamonix is only about 3400 feet.
You might briefly go a lot higher.
The top of the cable car at Chamonix is over 12,000 feet.
The Jungfraujoch is 11,400 feet.
As I said earlier, the Zugspitze is under 10,000 feet.
You'll probably go over Brenner Pass, at 4600 feet, to get to the Dolomites.
But even if you go up to those elevations, you won't be staying there for long.
Just take it easy. Don't over-indulge. You should be fine.
BTW, I live outside of Denver, at about 5400 feet.
Thanks all for the responses. We will take it easy, hiking is our main goal, but a good brown beer or French wine in moderation is bound to happen.
When I'm in Europe I usually have a couple glasses of wine at dinner. I did that all through the Alpine tour. The Alpi di Suisi meadow is about 5200' which I've never had a problem with. We were only on the Zugspitze peak for a couple hours mid-day. Fussen is about 2500' so you do get a bit acclimated before the Lauterbrunnen Valley. No ascent there for our tour - the peaks were fogged in. I did feel the altitude at the summit of Aiguille de Midi in Chamonix but not enough to spoil it. Chamonix is the highest place you'll be overnight, and it's 4200' and at the end of the tour.
Drinking a lot of water helps me a lot. There was no potable tap water on Aiguille de Midi, maybe not on the Swiss peaks, either. Bottled water was exorbitantly expensive at the peak. Always have a bottle or two with you.