Is this phrase antiquated or dumb, or is it still in use?
Someone asked me what I do in the morning and I say I often 'surf the ‘net’. I don’t know what else to call it. Do I sound like an old dork?
I can only say that when I used the phrase to my wife about 6 months ago she reacted as if I was talking about driving to work in a Model T.
I think the kids today say “Cruising the information superhighway.”
I still say it… but mostly for comic effect. It’s a bit anachronistic I think.
That would actually be rather awesome. Driving to work in a Yugo…
I still type in “www” when I’m looking for a website.
The default state is now to be online. You really need to warn your friends and colleagues if there may be an interruption, as in: “I may be offline for a couple of hours next Tuesday afternoon for heart bypass surgery.”
If I sound like an old dork when I say it, it’s because I am.
I prefer “going wiki-wandering”, but whatever floats your boat.
If there is nothing interesting playing on the wireless and no new offerings at the picture show, I can usually be found surfing the net.
Actually I still say it routinely. I didn’t know it was considered outdated. And I work in the IT field. Also I am old.
(Safe for work, although the Millennials might not understand some of it.)
To really boost your geezer cred you need to state that you are surfing “the world wide web”.
I’m considering cranking up the horseless carriage to go to the general store for victuals. And perhaps firing off a Marconi-gram. As soon as I’m done surfing the intertubes.
Some just call it procrastinating. I used to play ‘just one more game’ of Bubble Shooter when I had some onerous task.
If not, I’m going to work it into conversations as much as I can.
That would be totally groovy. 
Come to think of it, a lot of the time I just say “I’m reading” or “checking the news” or something like that. I do still say “surfing the net” unironically. But I don’t do that much idle surfing anymore. I usually get online to read something specific. So if someone asks me what I’m doing, I often answer in the specific instead of just “surfing”.
That’s a good answer, I am usually checking Facebook or reading my usual daily list of interests. So that’s what I’ll say. (Just meandering around seeing what pops up was what I did years ago.)
Only the cool people.
It’s perfectly cromulent.
I was growing up (grade school and high school) just as this was all getting huge, even then only teachers said that.
Personally I say “I am monitoring the internet for subversive content.”