A few things...
As someone else mentioned, the top listings on Google all seem to reference "the best restaurants" or "the top 10 restaurants". Also, they typically mention the current year. Both of these encourage clicks, and if people are clicking your result, it'll help improve your ranking. So, change your titles to "The 10 Best Restaurants in Smithfield, Dublin - 2019" for area pages.
You also have no H1 tags on these pages. This is SEO 101. Add an H1 heading that says "Newtown Restaurants, Dublin" at the top of the area pages.
Your URL structure is...
https://www.menucosm.com/restaurants/smithfield-274
You're using 274 as an ID, but you would be better of making shorter URLs for both users and SEO, and using the name in the URL as the identifier. I'm assuming you can find a way to not have two areas in Dublin with the same name. The new URLs would just be...
https://www.menucosm.com/restaurants/smithfield
Think about adding a short description at the top of area pages. A tiny paragraph where you can talk about the area, what it's known for, the type of restaurants there, etc. You want to keep it minimal, because you don't want to distract from the list of restaurants, but it's a chance to plug some keywords, the area name, Dublin, etc.
You have very, very few restaurant ratings. This means I can't search for highly rated restaurants in my area, and you can't recommend restaurants when users are viewing one. Take the scores from Google, TripAdvisor, and Yelp, and generate scores for each of your restaurants. For example, if a restaurant is 4 stars on TripAdvisor with 10 ratings and 5 stars on Google with 1 rating, then you might say it's rated 4.1 on your site, or 82%. And just like that, your site becomes much more valuable, and the doors open for more features and filters. If you get enough traffic one day, you can start to include your own user reviews.
One of the first things I see on your restaurant pages is the link to the restaurant's official website. I imagine a lot of users bounce there, without ever realizing you have menus on your site. You might want to reverse that, and better highlight your menu pages.
On area pages, the filters are all hidden by default. That's a valuable part of the site users are likely overlooking. You might want to have them always visible, and organize them a bit better to remove some of the unnecessary white space (which is a bigger deal if they're always visible).
You have cuisine categories, but when I'm browsing the list of restaurants, I don't see them anywhere. When I see a restaurant like "Beo Kitchen" in the area list, it's meaningless. Is this a burger place? Fine dining? Sushi? Vegetarian? You have the category data, so display it beside the restaurant so users don't have to click each one and read the description to see if it's relevant to them.
With all that being said, this is not likely to be a success because it's such a competitive area and you're not improving on the existing competition that everyone is aware of. So, I wouldn't get carried away spending a ton of additional time on the project. The good news is that you have a site, it works, the design is simple and easy to use, there's data there, it's cheap to host, and it's ranking on Google for certain keywords and phrases. There's no reason not to make a few of the simple changes I mentioned, like the title tags and H1 tags. That could be a few minutes of work, and make a noticeable difference in a couple of months. I would not recommend advertising on Reddit or paying anywhere to promote it. I'm quite certain you'll be throwing money away. I suggest working on the SEO and a few minor improvements, and letting the site simmer for a year as you focus on other projects. You can see if the analytics rise in that time, and if you start seeing a few thousand users a month. For some perspective though, you probably need a 20x increase in traffic to earn a dollar a day from advertising.