1969 is an exceptional year for Dom Perignon. I have never had the wine- though interestingly I will be opening my one and only bottle in December, so will have a TN soon. From good storage, the 1964 and 1966 are still singing, so depending on the temperatures this endured it may well be quite good.
This bottle has some ullage, but to my thinking not too bad given its age. Ullage refers to the level of the fill. The measure varies depending on the type of wine and shape of the bottle. In champagne it is often measured from the bottom of the foil. To help us all a bit further in guiding you, if you have access to the bottle please measure the distance between the bottom of the foil capsule that covers the cork and top of the bottle and the fill level of the wine and report the measurement here.
Temperature will be a key issue, and it is especially problematic with Dom Perignon because the wine is so widely distributed in the United States, and back then would have been available at many liquor stores. Even if the recipient stored it well, you never know if it was purchased at release from a good retailer or if it was a gift that had sat for a few months on a store shelf. Importing practices were not so great then either. In this instance, location potentially works in your favor as the odds are a bit better than if you had found the bottle down here in Texas. To the extent you can, at least find out the approximate basement temperature in the home. Probably too late to get details of acquisition- but ask if you can.
Color is another key factor and must be evaluated in person by an expert who is well versed in the subtle differences in bottle color over the years as well as what good examples should look like. But at the least you should be able to see a light shining through from behind. If the wine is very dark in color or not even transparent- not good.
There should still be a very little bit of effervescence remaining as well. If you gently tip the bottle upside down and back up again, there should be just a few small bubble generated.
If you can establish the color is good, then it is time to make an offer. The prior poster is correct that the last two auction results for this were just over $900 including buyer’s premium. Prior to that, it was in $670 and $530 for the two 2018 sales reported. This is consistent with the 64 and the 69 though at slightly higher levels- there has been a strong uptick this year in the value of old champagne at auction. The most recent retail price I can report from a reputable London broker (the safest way to buy old Dom) is 425GPB- or around $550 USD, and that was within the last 2 months.
The bottle is something of a risk because you do not have strong assurances it was stored at 55 degrees or less its entire life. Provided you can get comfortable with the basement temperature being consistently below 60 degrees, you can find a local retailer or expert who can tell you the color is good, and if it passes the effervescence test I note above- then I think a reasonable offer on your part would be $400-500 for the bottle. If you cannot get satisfactory results on any one of these three “tests”, I would suggest passing entirely. Heat damaged Dom actually has some flavor and character to it as long as it has not been totally roasted, but once you have tried pristine bottles you will look back with revulsion on such experiences. When the wine is heat damaged and in old age, that lovely cream and light caramel texture becomes like drinking peppermint candies.
That price I suggested may seem a bit low, but keep in mind those 2 recent auction results included buyer’s premium- so at the most the original seller got net proceeds of around $750, and at that price I am assuming the bottles must have been in pristine condition or had impeccable provenance- neither of which apply here.