@minipenguin: Originally I thought ‘hell no!’ until you said that the 8k doesn’t include flights; now you’ve clarified, yes, it’s doable; JUST.
You’ve had some great tips above, and the ones I would reiterate are:
Shop around for accommodation; Trivago for example compares prices for you from different websites, and you can save a lot this way.
The big destinations (eg Rome, Paris, London, etc) will usually command higher prices; but, deals can still be found. For example, if you’re prepared to share a bathroom, you can get a hotel with great Trip Advisor ratings in the heart of Rome for just $45 per night B&B, or rooms with private bathrooms in Paris for around $90 (which is super cheaper for Paris). You will however likely need to be flexible. Greece has some very reasonably priced and perfectly lovely accommodation; think prices from $45 per night depending on the area and season.
Check out apartments/self-catered accommodation. This will give you more flexibility in terms of eating, as you woll be able to buy food in and prepare it in your apartment; when I travel to Europe, I always stay self-catered, and I buy food in for breakfast and lunch. Things like water, bread, cheese and fruits are super-cheap, likewise wine (bought a bottle of lovely sparkling wine in Paris for just $1.50 lol). If you stay B&B, you typically won’t have kitchen facilities so it will be harder to save money this way as you won’t really have anywhere to prepare lunch etc.
Food-wise, definitely try to make your own breakfast and lunch as I said above. As far as evening meals go, you should be able to eat decently in most cities for $50 between you, excluding drinks.
Plan your route prior to travel. Check out budget airlines like Easy Jet and Ryan Air for flights (just be aware that luggage isn’t included, so it can look cheaper than it is; still, a single should cost around $90 with luggage if you book early; flights are released 6 months in advance so look out for them), as well as British Airways, which can be reasonable and includes luggage. Also look into rail travel.
Get as many guide books as you can, and plan what you want to see. Some places, particularly in Italy, can be pricey in terms of entrance; plenty of places in France on the other hand can be very cheap, or free, so you can see a lot without spending a fortune.
IMPO you’ll likely be looking at around $60 a night on average for accommodation (based on staying as cheaply as possible and not spending too much time in the more expensive cities) or a total of $2500. Food-wise, I think you’d need to budget around $10-15 per day if you self-cater for breakfast and lunch, and around $50 a day for dinner; so, around $2750. That would leave you with around $2750 for travel between destinations, entrance fees, and luxuries like alcoholic drinks.
My personal opinion is that I’d go for 4-5 weeks so I wasn’t scrimping the whole time; while doable, it will be tight, and you won’t be able to enjoy many luxuries, and will likely be constantly watching the pennies. I prefer to be a little more relaxed so would choose to go for less time but not feel so cash-strapped than go for longer but be stressing about how much that glass of wine with dinner might affect our budget.