You can run “actual C++” on AVR boards, the language used to program AVR-based Arduinos is C++. The avr-gcc toolchain simply doesn't include the C++ standard library, because some parts of the standard library use a lot of dynamic allocations, or include design decisions and optimizations that make sense on a 32-or 64-bit CPU with megabytes or gigabytes of RAM, but not on an 8-bit AVR processor with 2KiB of RAM. Many other parts of the standard library would work just fine on AVR, but there's simply no point in maintaining a standard library implementation for a relatively niche 8-bit microcontroller that's quickly losing its popularity in favor of cheaper and much more powerful 32-bit ARM, RISC-V and Xtensa cores.
If you go to https://www.arduino.cc/en/Main/Products, most boards in the “Enhanced features” and “Internet of Things” categories have an ARM chip. The architecture is mentioned on the product page for each board and in the technical specifications. Do keep in mind that there's a wide range of different ARM cores. A Cortex-M4 will be much more powerful than a Cortex-M0(+), for example, and some chips might have an FPU to perform floating point operations in hardware, etc.
I personally like the Teensy boards, the 4.x line has a Cortex-M7 clocked at 600 MHz with a 64-bit FPU, it's (one of) the fastest microcontrollers you can get right now, and a Teensy 4.0 is the same price as an Arduino Nano.
Which board is suitable for your project will depend on your application. If you're not going to do any real-time digital signal processing like audio, video, advanced control algorithms etc. having a 600 MHz microcontroller with an FPU is pretty pointless. If you need wireless communication, it might be worth looking into Nordic or Espressif chips with built-in Bluetooth or WiFi. If you just need a small microcontroller to control some LEDs/motors and read some basic sensors, maybe as an upgrade from an Arduino Nano, a Cortex-M0 will be just fine.
On the other hand, for a hobby project that will never be mass-produced, there's nothing wrong with using a microcontroller that's more powerful than strictly needed. Spending a couple of dollars more is a better idea than finding out after weeks of work that the chip you bought doesn't have enough resources for your project.