Getting elevation at lat/long from raster using python?

Here's a more programmatic way of using GDAL than @Aragon's answer. I've not tested it, but it is mostly boiler-plate code that has worked for me in the past. It relies on Numpy and GDAL bindings, but that's about it.

import osgeo.gdal as gdal
import osgeo.osr as osr
import numpy as np
from numpy import ma

def maFromGDAL(filename):
    dataset = gdal.Open(filename, gdal.GA_ReadOnly)

    if dataset is None:
        raise Exception()

    # Get the georeferencing metadata.
    # We don't need to know the CRS unless we want to specify coordinates
    # in a different CRS.
    #projection = dataset.GetProjection()
    geotransform = dataset.GetGeoTransform()

    # We need to know the geographic bounds and resolution of our dataset.
    if geotransform is None:
        dataset = None
        raise Exception()

    # Get the first band.
    band = dataset.GetRasterBand(1)
    # We need to nodata value for our MaskedArray later.
    nodata = band.GetNoDataValue()
    # Load the entire dataset into one numpy array.
    image = band.ReadAsArray(0, 0, band.XSize, band.YSize)
    # Close the dataset.
    dataset = None

    # Create a numpy MaskedArray from our regular numpy array.
    # If we want to be really clever, we could subclass MaskedArray to hold
    # our georeference metadata as well.
    # see here: http://docs.scipy.org/doc/numpy/user/basics.subclassing.html
    # For details.
    masked_image = ma.masked_values(image, nodata, copy=False)
    masked_image.fill_value = nodata

    return masked_image, geotransform

def pixelToMap(gt, pos):
    return (gt[0] + pos[0] * gt[1] + pos[1] * gt[2],
            gt[3] + pos[0] * gt[4] + pos[1] * gt[5])

# Reverses the operation of pixelToMap(), according to:
# https://en.wikipedia.org/wiki/World_file because GDAL's Affine GeoTransform
# uses the same values in the same order as an ESRI world file.
# See: http://www.gdal.org/gdal_datamodel.html
def mapToPixel(gt, pos):
    s = gt[0] * gt[4] - gt[3] * gt[1]
    x = (gt[4] * pos[0] - gt[1] * pos[1] + gt[1] * gt[5] - gt[4] * gt[2]) / s
    y = (-gt[3] * pos[0] + gt[0] * pos[1] + gt[3] * gt[2] - gt[0] * gt[5]) / s
    return (x, y)

def valueAtMapPos(image, gt, pos):
    pp = mapToPixel(gt, pos)
    x = int(pp[0])
    y = int(pp[1])

    if x < 0 or y < 0 or x >= image.shape[1] or y >= image.shape[0]:
        raise Exception()

    # Note how we reference the y column first. This is the way numpy arrays
    # work by default. But GDAL assumes x first.
    return image[y, x]

try:
    image, geotransform = maFromGDAL('myimage.tif')
    val = valueAtMapPos(image, geotransform, (434323.0, 2984745.0))
    print val
except:
    print('Something went wrong.')

Check out my answer here... and read here for some information. The following info was taken from Geotips:

With gdallocationinfo, we can query the elevation at a point:

$ gdallocationinfo gmted/all075.vrt -geoloc 87360 19679

The output of the above command has the form:

Report:
   Location: (87360P,19679L)
Band 1:
   Value: 1418

This means, that the elevation value at the provided geolocation is 1418.