This is a difficult question! I have many from that price range-- most of my collection so far consists of coins in the ~$15-$200 range. I love them all. Admittedly though, many coins in my collection came from large mixed lots so the price is low due to quantity (and quality is not high). More recently I've moved to acquiring fewer coins of higher quality and/or rarity.
Instead of showing one favorite or recommendation, I've somewhat randomly selected fifteen of my coins which are in that price range. Images are not to relative scale.

Left to right, top to bottom:
1. SICILY, Syracuse. AE tetras, 14mm. 390 BC
2. THRACE, Chersonesos. AR hemidrachm, 13mm, 400-350 BC
3. EUBOIA, Histiaia. AR tetrobol, 13mm. 340-330 BC
4. ARGOLIS, Argos. AR hemidrachm, 13mm. 330-270 BC
5. SELEUKID KINGS, Seleukos I. AR tetradrachm in the style of Alexander the Great, 27 mm. 295-291 BC
6. IONIA, Klazomenai. AR diobol, 9mm. 499-494 BC
7. PTOLEMAIC KINGDOM OF EGYPT, Ptolemy II. AE obol, 22 mm. 285-246 BC
8. KINGDOM OF PERSIS, Unknown king, possibly Vadfradad (Autophradates) II. AR hemidrachm. Mid-second century BC
9. ROMAN REPUBLIC, moneyer L. Postumius. AR denarius. 131 BC
10. PHOENICIA, Arados. Trajan. AE 22mm. 116/7 AD
11. THRACE, Pautalia. Caracalla. AE 29mm, 198-217 AD
12. MOESIA INFERIOR, Marcianopolis. Macrinus, with Diadumenian. AE 27mm. 217/8 AD
13. EGYPT, Alexandria. Antoninus Pius billion tetradrachm, 24 mm. 138/9 AD
14. EGYPT, Alexandria. Claudius II Gothicus potin tetradrachm. 268 AD
15. ROMAN IMPERIAL, Trajan. AR denarius, 18 mm. 101-102 AD
For some reason I left out a slew of my favorite Ptolemaic bronzes. Those certainly give a lot of bang for the buck. I love the type and have a dozen or more. Unless you're shooting for super quality or gargantuan size (>40mm) you will be able to find scores of examples in your desired price range. Here's an example of a 42mm from Ptolemy VI although it did cost more than your desired price. I must've misfiled my other pictures of similar examples from your price range.

Edited to add: of the pictured coins, only two were "blind" purchases from large mixed lots (the Trajan denarius and the Postumius denarius, which cost ~$15 each).