Alright, admission time… I’ve never been on a plane. And have never travelled outside of Europe.
To begin with, I was like you, OP. I was afraid of flying (and have a serious phobia of heights that gives me a horrendous physical reaction – panic attacks, dizziness, loss of vision and eventually passing out.)
This was my main reason for never travelling very far in my childhood, teens and early twenties but then, as I became more environmentally aware, I realised that not flying was a good thing for the environment. I stopped being embarrassed about it and stopped trying to change the way I felt about it or get on a flight.
I’m now happily a non-flier entirely for environmental reasons. I’ve only travelled outside the UK once in the past 5 years (to France). I don’t drive and choose to either cycle/walk or use public transport. I don’t eat meat, and try where possible to eat seasonally and locally grown food (though this can be very difficult at times!) I also don’t have my own children, I recycle, I use everything until it’s literally falling apart and can’t be mended/repaired. I went back to uni to study ecology, environmental science and geology, hoping that maybe one day I can do something - anything.
It makes me extremely angry to hear of regular business trips round the world, just for ‘networking’ purposes or for one bloody meeting. With skype and the level of communication we have now thanks to technology there’s absolutely no need for it.
And travelling long-haul regularly, just to sit on a beach or visit a resort? No, it’s selfish, pointless and people need to change their outlook sharpish if we want to make any kind of dent on climate change.
Our current way of life and attitudes globally to travel, food production, industry, consumerism and waste are completely unsustainable. We can all keep on as we are and say ‘Oh there’s no point because X,Y,Z country is doing A,B and C!’ but, personally, I need to feel like I’m at least making some effort to change my ways and do what I can for future generations, or I couldn't live with myself.
I really don't think the majority of people fully grasp just how fucked we are and how close to the edge our environment is 
So yes, I would make those journeys without flying – but only if I really had to. Otherwise I just wouldn’t be making those journeys at all.