Before you spend $ or time marketing your service / website, ensure that your brand itself is quite strong.
For example, if your name or domain is awkward, ambiguous, or off-putting, then every dollar and hour you spend promoting your brand will work less efficiently in your favor than if you were spending the same amount of money and time marketing something more robust and attractive.
Totally understand this problem, since we faced it very early on. I helped grow our travel community from 0 to over 70,000 travelers in less than a year and worked with JetBlue and Lufthansa Ventures at the accelerator that Dropbox and Paypal came from and this question came up over and over.
My best advice for you would be to create a brand around your business instead of competing with the Expedia's and Kayak's of the world for paid advertising space.
What this looks like in practice is essentially pivoting your social media strategy into a travel influencer brand that offers travel content to its audience and builds depth with the travel community. The difference between this and what someone like Kayak is doing is the following:
Paid advertising scenario:
Sally wants to fly. She goes to Google and types "flights to Houston". You can't outspend Kayak for this search. If your strategy depends on SEO or PPC, you're dead.
Sally wants to fly. She goes to the website of the famous YouTuber/Instagramer who has a travel app that she's always wanted to try out. She willingly consumes their travel content daily because it's fun, entertaining, and it makes her want to travel more.
You can only win on the branding scenario. It plays to your unfair advantages/disadvantages. You don't have money to compete with Expedia on PPC, but unlike Expedia, you as the CEO of the startup can curate or create content that is much more informal (memes, Q&A's, funny videos, travel bloggers) that gets you in front of your audience every day.
Happy to talk more about your business!
Your best bet for creating fast growth is to try and get the people who currently promote your competitors to convert to your service.
For example, start showing domain expertise in places like Reddit's /r/digitalnomad and /r/travel, hashtagnomads.com, nomadforum.io, and other sites where people are frequently asking questions about (and actually booking) flights and hotels.
Once you've developed a reputation, you can start working on partnerships with key influencers in the space (affiliate links, etc.) to encourage more links and referrals to your service.
I used this strategy, along with strong inbound marketing on the site itself, to grow a digital agency to the point it couldn't take on additional work.
Feel free to hit me up for a call if I can answer any follow-up questions or go over specific strategies.
Developing the initial critical mass in place to entice normal consumers to stick with your site is critically important. Naturally I'd recommend reaching out to your existing social circle to generate a base of user content, usage, reviews, and feedback. Beyond those circles, have you considered reaching out to teams abroad to generate activity from their local regions of interest? This could be a great way to build activity from local experts, and avoid any diluted fluff.
Feel free to reach out to me to discuss more, I'd be happy to consult. Also, you may be interested to hear about my most recent epic travel adventure, to run the 2015 Pyongyang, North Korea marathon.
You have to collaborate with influencers (YouTubers, Instagrammers) or complementary companies (luggage, travel pillows, etc.) with a bigger audience than you. If they recommend your site in their blog or video and vice versa, then that will grow your audience.