My personal setup is a server in my parents basement ~4 miles away (we don't get floods or hurricanes, or anything that would likely destroy both locations, just blizzards). My files automatically backup via the Internet to their house. If I have to restore my 700GB of data, I just drive over, pop a new HDD in the server, restore to it, and then put it in my server.
Four miles is a bit too close for comfort. The industry recommendation is usually 20km (13 miles) - this may have changed since I last was working on this sort of thing. When the Canberra bushfires (
http://en.wikipedia.org/wiki/2003_Canberra_bushfires) occurred (over 500 houses destroyed), one of the Commonwealth Departments had the fire come to the back door (which was burnt) of its computer centre, and to the fence (also burnt) of its backup facility over 30km away. With climate change, the frequency and severity of extreme climatic events (including blizzards) is changing these sorts of figures. Places that had no fire problems 40 years ago are now having those problems. 40 years ago, no-one would have considered Canberra vulnerable.
I also shook my head at the number of people who have backups in their basements. The two most common places for computer centres used to be basements (which got flooded) and immediately above the corporate cafeteria (the most likely place for fire - which travels up). The gear takes up so little space in the home these days that surely a more appropriate place can be found. Even basements at the top of a hill can be flooded.
As others have said, how much space do your pictures take? My favourite way to backup this stuff would be to use a USB stick, periodically, and send the USB stick to a relative who lives more than 20km away. This way, you know that that everything you want is on the stick, and if you accidentally delete some of your pictures they are safe. USB sticks are cheap enough that you can use a new one each time, and they seem to be growing in size in line with our disk usage.
There are a lot of backup disks on the market - we currently have a 3TB WIFI backup that is not located in the same room as the computer (again, if you have a house fire, you don't want your backup going with your computer). Remember that even if a fire doesn't damage electronics, smoke damage may. I tend to believe that a hidden WiFi setup is best, as this is more likely to remain in case of burglary (another main risk). I also like my backup to be on a different circuit, and preferably a different power phase. And all my equipment is on some sort of surge protector. Solid state disks should be more robust than other types of disk.
I don't like memory cards, as there are a lot of formats, and they tend to become obsolete more quickly than USB sticks. This is also a reason I don't put my precious memories on only one media - digital media tend to become obsolescent very quickly, and unpopular media such as backup disks and old memory card formats tend to become obsolescent more quickly than popular media. I'm sure you remember some that have become obsolete.
I don't like the cloud for personal reasons but it is probably a good option. One problem with it is that you could forget the password, and not be able to access it.
Oh, by the way, I spent too many years working in this area of computing before I retired four years ago. I have seen too many damaged computers (including by earthquake in Australia - which never gets earthquakes) and too many computer problems that happened just because people didn't think.
Please don't have just one backup - and don't delete it to write another one over the top of the previous one. One of my early experiences was of a computer centre where they valued backup tapes so much they only had one set, and backed up over the top of the previous backup. When you are backing up a whole disk, you are probably exercising it more than you are at other times, and the most likely time for a disk to fail (in my experience) is when it is being backed up. Unfortunately that happened to the computer centre I am remembering. Recovery was not pleasant - the company's computers were out for 3 weeks.