Well firstly, "the newest Google standards" actually discourage basing your SEO campaign on pure link-building. To avoid the eventual "Google hammer", you should start by focusing on generating natural traffic over generating a bunch of links - if you do that right, you can then activate your own users to share your links themselves and start gaining press traction as well.
Plus, Google's search results are moving more & more away from the basic notion of "whoever has the most links with the right keyword ranks highest", and more towards "the website that provides the best data & content will be ranked highest". That doesn't mean link building is dead, it just changes the strategy from what most people think of when they say link-building. There are still plenty of viable techniques though:
- Press: Signing up for a service like HARO is time-consuming, but if you keep it up you can generate several organic press mentions & likely even interviews. I don't know your travel company's SEO/marketing budget, but press releases with a good angle can be a great source of these as well.
- Social backlinking: I'm not talking about just basic Facebook/Twitter marketing here...there are a lot of other options to create social authority figures that people come to/subscribe to. Group Pinterest boards, services like Paper.li, Scoop.it, etc.
- Q&A - Ever considered a Reddit AMA (Ask me Anything)? I haven't researched travel-related subreddits before, but I've done these for other companies I've worked with and it always generates at *least* a boost in traffic and usually a number of signups.
- Guest blogs: Careful with these, Google's been cracking down on guest blog networks & spammy blogging techniques lately - but they can still generate traffic when used properly.
Also, if you haven't already, make sure you've got your deals marked up with proper schema. It's easier (and in my opinion soon to be the primary method) to get links & traffic from Google when your website is providing data to the Knowledge Graph. Let me know if you've got any questions.