What is a basic object detection/localization ML algorithm that can be used for my relatively simple image set?
So, the following techniques are used for object detection (other can YOLO, R-CNN and other Deep Learning Techniques):

Haar Cascade Classifier

This was the first facial detection algorithm to be successfully used and is popular until today. Proposed by Viola and Jones in their paper Rapid Object Detection using a Boosted Cascade of Simple
Features (2001, CVPR) this algorithm uses Haar-like features from integral images and a cascade of boosting classifiers to detect objects in images. Lienhart proposed in 2002 a improvement to this algorithm in his paper Empirical Analysis of Detection Cascades of Boosted Classifiers for Rapid Object Detection

It can be easily trained using OpenCV Object Detection Module in Python, C and Java, also available in Matlab Computer Vision Tool Box as vision.CascadeObjectDetector and probably many other platforms.

Max-Margin Object Detection

Proposed in the paper Max-Margin Object Detection by Davis E. King, creator of dlib, where it has been implemented, this algorithm has implementations for face detection using HoG Features and CNNs features.

The abstract of the paper goes:


  Most object detection methods operate by applying a binary classifier
  to sub-windows of an image, followed by a non-maximum suppression step
  where detections on overlapping sub-windows are removed. Since the
  number of possible sub-windows in even moderately sized image datasets
  is extremely large, the classifier is typically learned from only a
  subset of the windows. This avoids the computational difficulty of
  dealing with the entire set of subwindows, however, as we will show in
  this paper, it leads to sub-optimal detector performance.
  
  In particular, the main contribution of this paper is the introduction
  of a new method, Max-Margin Object Detection (MMOD), for learning to
  detect objects in images. This method does not perform any
  sub-sampling, but instead optimizes over all sub-windows. MMOD can be
  used to improve any object detection method which is linear in the
  learned parameters, such as HOG or bag-of-visual-word models. Using
  this approach we show substantial performance gains on three publicly
  available datasets. Strikingly, we show that a single rigid HOG filter
  can outperform a state-of-the-art deformable part model on the Face
  Detection Data Set and Benchmark when the HOG filter is learned via
  MMOD.


I think these are the two most relevant outside of Deep Learning, reading the related work fromt he 3 cited articles might give you some light on how to proceed.