The only place I've gone outside the US was Ireland; it was earlier this year. We did a bus tour for the first week which took us basically around the outside edge of the country (saw a lot of the major sights - Glendalough, Waterford Crystal, Blarney Castle, the Ring of Kerry drive, Cliffs of Moher, Giant's Causeway, etc), and then for the second week and a half my friend and I traveled on our own: we went to the west side of the country (stopping at the
Rock of Cashel on the way) and stayed in a tiny town called Cahersiveen on the southwest coast so that we could go to the
Skellig Islands (if you've seen Star Wars: The Force Awakens, it's the island where the final scene was filmed), and then we spent the last few days in Dublin.
As far as ways to make it cheaper:
- Look into B&Bs and hostels instead of hotels. (There's also a site called AirBnB if you're so inclined, which is where random people literally rent a room/couch of their home, but I preferred going with actual businesses).
Anyway, bed-and-breakfasts are big in Ireland, not sure about other places so much, but they're generally cheaper than hotels. The one we stayed in was about $35/person/night and she made us a hot breakfast each morning (also did laundry and drove us a couple places for an extra cost.)
Hostels are more of a Europe thing in general: they're basically really cheap, bare-bones hotels. We spent a couple nights in one on the way to the west side of the country and then the same one again on the way back east. Now, note that usually hostels have dormitory-style rooms, sometimes gender-specific, sometimes not; you'll need to look at ones where you're traveling and see what they offer (and look at reviews to make sure it doesn't look sketchy). Sometimes though they may offer private rooms. The one we stayed at offered them, so that's what my friend and I did: basically it was just like a simple hotel room (even had a lock like one), nothing in it but the beds and a shelf and light on the wall and a bathroom. The beds were hard, and breakfast was nothing special (basically just raisin bran or toast, you server yourself and wash your own dishes), but it was breakfast and a place to sleep, and it was cheap (like $20-25/person/night; dormitory rooms are cheaper even than that), and it was kinda nice since everyone else there was mostly around college age too.
- Consider buying groceries. While I definitely do recommend eating at restaurants and trying things local to the area (make sure you save money just for food!), you can save costs by getting groceries and making a few of your own meals. (It's also kinda fun to see how different grocery stores are compared to home.)
- Some places may offer day tours; that can be a way to see some sights without having to go on a big fancy tour.
I'd definitely recommend reading about where you're traveling (books about the country, online, etc). Search for "(place name) tours" online and check out places where the tours stop to get an idea of good locations to visit, even if you don't intend to actually go with a tour. You can also go to a travel agent: if they're like mine, then there's no charge to go in and ask about things and pick up trip catalogs. They get a commission from the travel company, so we didn't have to pay them anything since it was the travel company paying them (they said the only way we'd have to pay anything is if we, like, only used their services to book a flight or hotel or something - which we did for the part of the trip after the bus tour, but since we also bought an actual tour we didn't have to pay for them).
I definitely recommend Ireland as a place to travel; it is absolutely amazing. It's one of the safest countries in the world, everyone's real friendly there, and it's and easy to get around (they have excellent bus/train systems that can get you just about anywhere you want in the country - bus rides are like $15-30 each and our train ride all the way across was about $25, but definitely book train tickets online 'cause it's a lot cheaper. Buses don't matter so much.) There's so much beautiful scenery and so many things to see: we spent two and a half weeks total, but we felt like we ran out of time. If you want to know specific tips about Ireland or want to know where to stop, I'm your girl.
I do want to go there again sometime - possibly over seeing other places in the world - and I'd even do it on my own. I think if I went again I'd just stay in B&Bs/hostels and travel to see a few things I missed (heck, I could do some of those on day tours), or maybe see more of things that I'd have liked to have spent longer at. Perhaps just a few free days too: a lot of our trip was spent running from one place to the next - when we stopped at places on the bus tour, it was enough time to see the high points of places - don't get me wrong, I don't regret doing it at all; it was a cool way to experience so much in so little time and the people were great - but looking back I think some of my favorite days were the unscheduled ones, when we could just explore, chat with the locals, and relax a bit, and get to really experience the town/city.