I love funky old things, been an avid flea market/antiques market hound since I was a very small child...blame it on my parents! And there are fascinatingly different things to be found abroad, so the first thing I research when planning a trip is markets & shops. I always bring cash for the markets, and come prepared with tape and bubble wrap in case it's needed to get something fragile home--and those things always go in my carry-on...I routinely come home from Budapest's Ecseri piac with a good 20+ lbs of pottery :)
Re haggling: I bring cash as I consider it rude to haggle and then whip out a credit card. I tend to have a good idea of an item's value and if it's reasonably priced I do not haggle. Depends entirely on the item & situation--most things I have never seen before and likely never again, so if it speaks to me, I buy it. I also print out a purse-sized table of conversion if I am going somewhere with non-Euro or pounds currency, like Hungary.
My favorite is Ecseri piac in Budapest, a 30 minute bus ride from central Budapest. Saturday is best, get there early as they pack up around 1 pm. It's a crazy ramshackle place, not too big, never crowded, some fixed shops, some indoor, some outdoor. I collect 1930s Hungarian pottery and there's always plenty of it, plus a lot of other unusual vintage things. Sellers are friendly--one invited me to have gulyas at his mother's house--but though little English is spoken it's still possible to bargain.
On a trip to Paris in 2016 I did not get to Clignancourt but instead went to Porte des Vanves and absolutely loved it--all outdoors, just around the corner from the Metro, just the right amount of vendors, all wonderful old things, dealers were pleasant and open to bargaining.
In Amsterdam there is the IJ-Hallen flea market, accessed by a free ferry ride from the Centraal train station. It was a cold rainy day and I found acres of used clothing, shoes and purses and not more than a few rows of vintage vendors so I headed back to town and found an antiques co-op that was chock full of great things.
In Vienna I went to the Flohmarkt at the Naschmarkt--different sections made it easy to find just the vintage dealers, there were also clothing and new item sections. Super crowded and you need to be very mindful of your purse/wallet.
Portobello Road in London on a Saturday has an enormous market--starts with antiques, then food vendors, then a big area of used records and clothing, plus the street has numerous charity shops and I really enjoy them, found some great clothing over the years. It can get very crowded.
Munich had several markets and I tried to find 3 of them--only made it to one and I can't recall the name, it was just outside a U station and quite large--mainly clothing and household items. It was very hot and I was in terrible pain from a lower back flare-up so not my best day for riding public transit and finding flea markets!
If you ever get to the San Francisco area on the first Sunday of the month I am absolutely blessed to have a fabulous antiques market right in my town of Alameda--the market is called Alameda Point Antiques Faire and it's held on our old Navy base, usually 600-800 dealers--all vintage, including a good amount of clothing and accessories.