This should do the job. String match with Levenshtein_distance.

pip install thefuzz[speedup]

import pandas as pd
import numpy as np

from thefuzz import process

def fuzzy_match(
    a: pd.DataFrame, b: pd.DataFrame, col: str, limit: int = 5, thresh: int = 80
):
    """use fuzzy matching to join on column"""

    s = b[col].tolist()

    matches = a[col].apply(lambda x: process.extract(x, s, limit=limit))
    matches = pd.DataFrame(np.concatenate(matches), columns=["match", "score"])

    # join other columns in b to matches
    to_join = (
        pd.merge(left=b, right=matches, how="right", left_on="City", right_on="match")
        .set_index(  # create an index that represents the matching row in df a, you can drop this when `limit=1`
            np.array(
                list(
                    np.repeat(i, limit if limit < len(b) else len(b))
                    for i in range(len(a))
                )
            ).flatten()
        )
        .drop(columns=["match"])
        .astype({"score": "int16"})
    )
    print(f"\t the index here represents the row in dataframe a on which to join")
    print(to_join)

    res = pd.merge(
        left=a, right=to_join, left_index=True, right_index=True, suffixes=("", "_b")
    )

    # return only the highest match or you can just set the limit to 1
    # and remove this
    df = res.reset_index()
    df = df.iloc[df.groupby(by="index")["score"].idxmax()].reset_index(drop=True)

    return df.drop(columns=["City_b", "score", "index"])

def test(df):

    expected = pd.DataFrame(
        {
            "City": ["San Francisco, CA", "Oakland, CA"],
            "Val": [1, 2],
            "Geo": ["geo1", "geo1"],
        }
    )

    print(f'{"expected":-^70}')
    print(expected)

    print(f'{"res":-^70}')
    print(df)

    assert expected.equals(df)


if __name__ == "__main__":

    a = pd.DataFrame({"City": ["San Francisco, CA", "Oakland, CA"], "Val": [1, 2]})
    b = pd.DataFrame(
        {"City": ["San Francisco-Oakland, CA", "Salinas, CA"], "Geo": ["geo1", "geo2"]}
    )

    print(f'\n\n{"fuzzy match":-^70}')
    res = fuzzy_match(a, b, col="City")
    test(res)

Update: the fuzzywuzzy project has been renamed to thefuzz and moved here

You can use thefuzz package and the function extractOne:

# Python env: pip install thefuzz
# Anaconda env: pip install thefuzz
# -> thefuzz is not yet available on Anaconda (2021-09-18)
# -> you can use the old package: conda install -c conda-forge fuzzywuzzy

from thefuzz import process

best_city = lambda x: process.extractOne(x, df2["City"])[2]  # See note below
df1['Geo'] = df2.loc[df1["City"].map(best_city).values, 'Geo'].values

Output:

>>> df1
                City  Val   Geo
0  San Francisco, CA    1  geo1
1        Oakland, CA    2  geo1

Note: extractOne return a tuple of 3 values from the best match: the City name from df2 [0], the accuracy score [1] and the index [2] (<- the one I use).